Quiz On Phase Diagrams

1. Steel, which consists of Iron (metal) and Carbon (non-metal), can be considered as an alloy.

True

False

Steel is indeed considered as an alloy because it is a mixture of iron and carbon. An alloy is a solid solution or a mixture of two or more metals, or a metal and a non-metal. In the case of steel, iron acts as the main component, while carbon is added in varying amounts to enhance its strength and other properties. This combination of iron and carbon gives steel its unique characteristics, making it a widely used material in various industries. Therefore, the statement is true.

Explanation

Steel is indeed considered as an alloy because it is a mixture of iron and carbon. An alloy is a solid solution or a mixture of two or more metals, or a metal and a non-metal. In the case of steel, iron acts as the main component, while carbon is added in varying amounts to enhance its strength and other properties. This combination of iron and carbon gives steel its unique characteristics, making it a widely used material in various industries. Therefore, the statement is true.

2. Segregation is the composition gradient in each grain of the solid solution, from the middle to the boundaries.

True

False

This statement is true because segregation refers to the uneven distribution of elements or impurities within a solid solution. In each grain of the solid solution, there is a composition gradient, meaning that the concentration of elements or impurities gradually changes from the middle of the grain to its boundaries. This can occur due to various factors such as diffusion or solidification processes.

Explanation

This statement is true because segregation refers to the uneven distribution of elements or impurities within a solid solution. In each grain of the solid solution, there is a composition gradient, meaning that the concentration of elements or impurities gradually changes from the middle of the grain to its boundaries. This can occur due to various factors such as diffusion or solidification processes.

3.

iv. The amount of the eutectic (Si) phase.

452.63 g.

6.26 g.

34.82 g.

81.44 g.

The correct answer is 452.63 g. This means that the amount of the eutectic (Si) phase is 452.63 g.

Explanation

The correct answer is 452.63 g. This means that the amount of the eutectic (Si) phase is 452.63 g.

4.

A Germanium (Ge)-Potassium (K) alloy, whose mass is 1000 g, is slowly cooled to a temperature that is just below 575°C. It was then discovered that it contains 615.38 g of pro-eutectic phase GeK. Find: i. The composition of the alloy.

40 % of K, and 60 % of Ge.

43 % of K, and 57 % of Ge.

45.38 % of K, and 54.62 % of Ge.

51.62 % of K, and 48.38 % of Ge.

31.15 % of Ge, and 68.85 % of K.

28.85 % of Ge, and 71.15 % of K.

26.15 % of Ge, and 73.85 % of K.

20.85 % of Ge, and 79.15 % of K.

The composition of the alloy can be determined by calculating the mass percentage of each element present. The mass of GeK is given as 615.38 g, which is 61.538% of the total mass of the alloy (1000 g). Therefore, the remaining mass of the alloy is 38.462%. Since Ge and K are the only elements present, this remaining mass must be divided between them. Since GeK is a binary alloy, the remaining mass must be divided in the same ratio as the atomic masses of Ge and K, which are 72.63 and 39.10 respectively. By calculating the mass percentage, it is determined that the alloy contains 40% K and 60% Ge.

Explanation

The composition of the alloy can be determined by calculating the mass percentage of each element present. The mass of GeK is given as 615.38 g, which is 61.538% of the total mass of the alloy (1000 g). Therefore, the remaining mass of the alloy is 38.462%. Since Ge and K are the only elements present, this remaining mass must be divided between them. Since GeK is a binary alloy, the remaining mass must be divided in the same ratio as the atomic masses of Ge and K, which are 72.63 and 39.10 respectively. By calculating the mass percentage, it is determined that the alloy contains 40% K and 60% Ge.

5. If an alloy consists of completely soluble solid solution between Germanium and Silicon, then it has one phase.

True

False

If an alloy consists of completely soluble solid solution between Germanium and Silicon, it means that the two elements are able to mix together at the atomic level and form a homogeneous mixture. In this case, the alloy will have a single phase because there is no separation or distinct regions within the material. Therefore, the statement "If an alloy consists of completely soluble solid solution between Germanium and Silicon, then it has one phase" is true.

Explanation

If an alloy consists of completely soluble solid solution between Germanium and Silicon, it means that the two elements are able to mix together at the atomic level and form a homogeneous mixture. In this case, the alloy will have a single phase because there is no separation or distinct regions within the material. Therefore, the statement "If an alloy consists of completely soluble solid solution between Germanium and Silicon, then it has one phase" is true.

6. The intermetallic compound is considered as a single phase alloy.

True

False

The intermetallic compound is considered as a single phase alloy because it consists of a single crystalline structure. Unlike other alloys that may have multiple phases, intermetallic compounds have a uniform composition throughout. This uniformity allows for consistent properties and behavior, making them distinct from other types of alloys.

Explanation

The intermetallic compound is considered as a single phase alloy because it consists of a single crystalline structure. Unlike other alloys that may have multiple phases, intermetallic compounds have a uniform composition throughout. This uniformity allows for consistent properties and behavior, making them distinct from other types of alloys.

7.

v. The weights of V and Si in the eutectic phases.

The correct answer is 27.96 g of Si in VSi2, 25.29 g of V in VSi2, 452.63 g of Si in (Si), and 0 g of V in (Si). This answer is correct because it follows the given information about the weights of Si and V in VSi2 and (Si). The other options do not match the given weights.

Explanation

The correct answer is 27.96 g of Si in VSi2, 25.29 g of V in VSi2, 452.63 g of Si in (Si), and 0 g of V in (Si). This answer is correct because it follows the given information about the weights of Si and V in VSi2 and (Si). The other options do not match the given weights.

8. Tungsten and Palladium are expected to have completely solubility in each other (both have atomic radius = 0.137 nm, Tungsten has a BCC crystal structure and Palladium has FCC crystal structure).

True

False

Tungsten and Palladium are not expected to have completely solubility in each other because they have different crystal structures (BCC for Tungsten and FCC for Palladium). The different crystal structures can hinder the mixing of the two elements, resulting in limited solubility rather than complete solubility.

Explanation

Tungsten and Palladium are not expected to have completely solubility in each other because they have different crystal structures (BCC for Tungsten and FCC for Palladium). The different crystal structures can hinder the mixing of the two elements, resulting in limited solubility rather than complete solubility.

9. In substitutional solid solution between A & B, an atom of A substitutes a void between the atoms of B.

True

False

In a substitutional solid solution, an atom of A does not substitute a void between the atoms of B. Instead, an atom of A replaces an atom of B in the crystal lattice structure. This substitution occurs when the sizes and chemical properties of A and B atoms are similar enough to allow for the exchange. Therefore, the correct answer is False.

Explanation

In a substitutional solid solution, an atom of A does not substitute a void between the atoms of B. Instead, an atom of A replaces an atom of B in the crystal lattice structure. This substitution occurs when the sizes and chemical properties of A and B atoms are similar enough to allow for the exchange. Therefore, the correct answer is False.

10. There is no probability to find a thermal arrest in an alloy's cooling curve.

True

False

Thermal arrest refers to the phenomenon where the cooling rate of a material slows down or stops completely during solidification. In the context of an alloy's cooling curve, thermal arrest can occur if there is a eutectic reaction or a phase transformation that requires a significant amount of time to complete. Therefore, it is possible to find a thermal arrest in an alloy's cooling curve, making the statement false.

Explanation

Thermal arrest refers to the phenomenon where the cooling rate of a material slows down or stops completely during solidification. In the context of an alloy's cooling curve, thermal arrest can occur if there is a eutectic reaction or a phase transformation that requires a significant amount of time to complete. Therefore, it is possible to find a thermal arrest in an alloy's cooling curve, making the statement false.

11.

iii. The weights of Mo and Zr in the eutectoid phases.

The given answer is correct because it provides the correct weights of Zr and Mo in both the eutectoid phases, Mo2Zr and (aZr). The weights of Zr and Mo in Mo2Zr are 33.49 g and 52.38 g respectively, while the weights of Zr and Mo in (aZr) are 590.93 g and 1.18 g respectively. This distribution of weights aligns with the composition of the eutectoid phases as per the given information.

Explanation

The given answer is correct because it provides the correct weights of Zr and Mo in both the eutectoid phases, Mo2Zr and (aZr). The weights of Zr and Mo in Mo2Zr are 33.49 g and 52.38 g respectively, while the weights of Zr and Mo in (aZr) are 590.93 g and 1.18 g respectively. This distribution of weights aligns with the composition of the eutectoid phases as per the given information.

12.

v. The weights of Fe and Nb in the pro-eutectic phase are:

0.67 kg of Nb, and 1.09 kg of Fe.

0.06 kg of Nb, and 1.17 kg of Fe.

0.86 kg of Nb, and 1.41 kg of Fe.

0.04 kg of Nb, and 0.69 kg of Fe.

0.44 kg of Fe, and 0.72 kg of Nb.

0.09 kg of Fe, and 1.76 kg of Nb.

0.87 kg of Fe, and 1.41 kg of Nb.

0.03 kg of Fe, and 0.69 kg of Nb.

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Explanation

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13.

iii. The amount of the pro-eutectic phase VSi₂.

494.13 g.

940.49 g.

55.97 g.

865.31 g.

116.55 g.

911.93 g.

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Explanation

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14.

The atomic weights for Gadolinium (Gd) and Magnesium (Mg) are 157.25 and 24.3 g/mol, respectively. For a 88.78 mol.% Mg alloy, that is cooled down to a temperature that is just above 821°K, select the correct answer(s): b) The amounts of the present phases are:

48.23 wt. % of liquid, and 51.77 wt. % of pro-eutectic (MgGd).

51.77 wt. % of liquid, and 48.23 wt. % of pro-eutectic (MgGd).

48.23 wt. % of eutectic, and 51.77 wt. % of pro-eutectic (MgGd).

51.77 wt. % of eutectic, and 48.23 wt. % of pro-eutectic (MgGd).

40.65 wt. % of liquid, and 59.35 wt. % of pro-eutectic (MgGd).

59.35 wt. % of liquid, and 40.65 wt. % of pro-eutectic (MgGd).

40.65 wt. % of eutectic, and 59.35 wt. % of pro-eutectic (MgGd).

59.35 wt. % of eutectic, and 40.65 wt. % of pro-eutectic (MgGd).

Based on the given information, the alloy is composed of 88.78 mol.% Magnesium (Mg) and the rest is Gadolinium (Gd). Since the temperature is just above the eutectic temperature (821°C), the alloy is not fully solidified and contains both liquid and solid phases. The correct answer states that 48.23 wt. % of the alloy is in the liquid phase, while 51.77 wt. % is in the pro-eutectic phase (MgGd). This means that the alloy has not fully transformed into the eutectic phase, and there is still a significant amount of liquid and pro-eutectic phase present.

Explanation

Based on the given information, the alloy is composed of 88.78 mol.% Magnesium (Mg) and the rest is Gadolinium (Gd). Since the temperature is just above the eutectic temperature (821°C), the alloy is not fully solidified and contains both liquid and solid phases. The correct answer states that 48.23 wt. % of the alloy is in the liquid phase, while 51.77 wt. % is in the pro-eutectic phase (MgGd). This means that the alloy has not fully transformed into the eutectic phase, and there is still a significant amount of liquid and pro-eutectic phase present.

15.

A Molybdenum (Mo)-Zirconium (Zr) alloy, whose mass is 1000 g, is slowly cooled to a temperature that is just below 738°C. It was then discovered that it contains 407.89 g of total Mo₂Zr phases. Find: i. The composition of the alloy.

75 % of Zr, and 25 % of Mo.

63.80 % of Zr, and 36.20 % of Mo.

70.44 % of Zr, and 29.56 % of Mo.

60.66 % of Zr, and 39.34 % of Mo.

95.24 % of Mo, and 4.76 % of Zr.

96.66 % of Mo, and 3.34 % of Zr.

96.20 % of Mo, and 3.80 % of Zr.

67.30 % of Mo, and 32.70 % of Zr.

Since the total mass of the alloy is 1000 g and the mass of the Mo2Zr phases is 407.89 g, the remaining mass must be the composition of the other elements. Therefore, the composition of the alloy is 75% Zr and 25% Mo.

Explanation

Since the total mass of the alloy is 1000 g and the mass of the Mo2Zr phases is 407.89 g, the remaining mass must be the composition of the other elements. Therefore, the composition of the alloy is 75% Zr and 25% Mo.

16.

ii. The amount of the eutectoid (aZr) phase.

592.11 g.

67.50 g.

517.12 g.

74.99 g.

350.59 g.

241.52 g.

218.12 g.

59.15 g.

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Explanation

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17.

An Vanadium (V)-Silicon (Si) alloy, whose mass is 1000 g, is slowly cooled to a temperature that is just below 1400°C. It was then discovered that it contains 53.25 g of eutectic VSi₂ phase. Find: i. The composition of the alloy.

74 % of Si, and 26 % of V.

92.47 % of Si, and 7.53 % of V.

55.03 % of Si, and 44.97 % of V.

73.50 % of Si, and 26.50 % of V.

51.75 % of V, and 48.25 % of Si.

45.14 % of V, and 54.86 % of Si.

51.36 % of V, and 48.64 % of Si.

44.75 % of V, and 55.25 % of Si.

The composition of the alloy can be determined by calculating the mass percentage of each element in the alloy. Since the mass of the alloy is given as 1000 g and the mass of the eutectic VSi2 phase is given as 53.25 g, the mass of the remaining alloy (V + Si) is 1000 g - 53.25 g = 946.75 g.

To find the percentage of Si, we divide the mass of Si by the total mass of the alloy and multiply by 100: (53.25 g / 946.75 g) * 100 = 5.62%.

Similarly, to find the percentage of V, we divide the mass of V by the total mass of the alloy and multiply by 100: (946.75 g - 53.25 g) / 946.75 g * 100 = 94.38%.

Therefore, the composition of the alloy is 5.62% Si and 94.38% V.

Explanation

The composition of the alloy can be determined by calculating the mass percentage of each element in the alloy. Since the mass of the alloy is given as 1000 g and the mass of the eutectic VSi2 phase is given as 53.25 g, the mass of the remaining alloy (V + Si) is 1000 g - 53.25 g = 946.75 g.

To find the percentage of Si, we divide the mass of Si by the total mass of the alloy and multiply by 100: (53.25 g / 946.75 g) * 100 = 5.62%.

Similarly, to find the percentage of V, we divide the mass of V by the total mass of the alloy and multiply by 100: (946.75 g - 53.25 g) / 946.75 g * 100 = 94.38%.

Therefore, the composition of the alloy is 5.62% Si and 94.38% V.

18.

ii. The amount of the eutectic phase.

505.88 g.

59.51 g.

134.69 g.

88.07 g.

The correct answer is 505.88 g. This suggests that the amount of the eutectic phase is 505.88 g.

Explanation

The correct answer is 505.88 g. This suggests that the amount of the eutectic phase is 505.88 g.

19. A eutectic reaction occurs by decomposing a liquid into two solid phases by cooling.

True

False

A eutectic reaction is a type of phase transition that occurs when a liquid mixture solidifies into two or more solid phases upon cooling. This process happens at a specific composition and temperature known as the eutectic point. Therefore, the statement that a eutectic reaction occurs by decomposing a liquid into two solid phases by cooling is true.

Explanation

A eutectic reaction is a type of phase transition that occurs when a liquid mixture solidifies into two or more solid phases upon cooling. This process happens at a specific composition and temperature known as the eutectic point. Therefore, the statement that a eutectic reaction occurs by decomposing a liquid into two solid phases by cooling is true.

20.

ii. The amount of the eutectic GeK phase.

199.43 g.

20.70 g.

71.23 g.

147.93 g.

217.39 g.

12.54 g.

64.32 g.

147.93 g.

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Explanation

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21.

ii. The weight of the pro-eutectic phase is:

1.76 kg.

1.24 kg.

2.27 kg.

0.73 kg.

1.15 kg.

1.85 kg.

2.28 kg.

0.72 kg.

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Explanation

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22.

iii. The weights of the eutectic phases are:

0.51 kg of e and 0.73 kg of (gFe).

1.04 kg of e and 0.72 kg of (gFe).

0.18 kg of e and 0.55 kg of (gFe).

1.72 kg of e and 0.55 kg of (gFe).

1.13 kg of m and 0.72 kg of (Nb).

0.72 kg of m and 1.13 kg of (Nb).

0.17 kg of m and 0.55 kg of (Nb).

1.73 kg of m and 0.55 kg of (Nb).

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Explanation

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23. The pro-eutectic phase is the phase inside the eutectic structure.

True

False

The pro-eutectic phase is not the phase inside the eutectic structure. The eutectic structure refers to the specific microstructure that forms when a eutectic alloy solidifies. The pro-eutectic phase, on the other hand, refers to the phase that forms before the eutectic reaction occurs. It is a precursor to the eutectic structure and is typically present in the alloy composition before the eutectic transformation takes place. Therefore, the statement is false.

Explanation

The pro-eutectic phase is not the phase inside the eutectic structure. The eutectic structure refers to the specific microstructure that forms when a eutectic alloy solidifies. The pro-eutectic phase, on the other hand, refers to the phase that forms before the eutectic reaction occurs. It is a precursor to the eutectic structure and is typically present in the alloy composition before the eutectic transformation takes place. Therefore, the statement is false.

24. A & B are two metals which are insoluble in the solid state. As temperature increases, the solubility limit increases.

True

False

The statement is false because as temperature increases, the solubility limit of most substances generally increases. However, in the case of A and B metals, their solubility limit does not increase with an increase in temperature. These metals remain insoluble in the solid state regardless of temperature.

Explanation

The statement is false because as temperature increases, the solubility limit of most substances generally increases. However, in the case of A and B metals, their solubility limit does not increase with an increase in temperature. These metals remain insoluble in the solid state regardless of temperature.

25. A peritectoid reaction occurs when a solid phase reacts with a liquid phase to produce a new solid phase.

True

False

A peritectoid reaction occurs when two solid phases react to produce a new solid phase, not when a solid phase reacts with a liquid phase. Therefore, the statement is false.

Explanation

A peritectoid reaction occurs when two solid phases react to produce a new solid phase, not when a solid phase reacts with a liquid phase. Therefore, the statement is false.

26.

iv. The weights of Fe and Nb in the eutectic phases are:

The given answer states the weights of Nb and Fe in the eutectic phases. It specifies that there are 0.19 kg of Nb in the eutectic phase (e), 0.31 kg of Fe in the eutectic phase (e), 0.04 kg of Nb in the intermetallic phase (gFe), and 0.69 kg of Fe in the intermetallic phase (gFe). This information provides the composition of the different phases in the system.

Explanation

The given answer states the weights of Nb and Fe in the eutectic phases. It specifies that there are 0.19 kg of Nb in the eutectic phase (e), 0.31 kg of Fe in the eutectic phase (e), 0.04 kg of Nb in the intermetallic phase (gFe), and 0.69 kg of Fe in the intermetallic phase (gFe). This information provides the composition of the different phases in the system.

27. Segregation can be eliminated by a heat treatment process called "quenching".

True

False

Quenching is a heat treatment process that involves rapid cooling of a material to increase its hardness. It does not have any direct effect on segregation, which refers to the non-uniform distribution of elements or impurities in a material. Therefore, the statement is false.

Explanation

Quenching is a heat treatment process that involves rapid cooling of a material to increase its hardness. It does not have any direct effect on segregation, which refers to the non-uniform distribution of elements or impurities in a material. Therefore, the statement is false.

28.

iv. The weights of Ge and K in the eutectic phases.

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Explanation

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29.

v. The weights of Ge and K in the pro-eutectic phase.

215.38 g of K, and 400 g of Ge.

238.46 g of K, and 146.16 g of Ge.

255.38 g of K, and 360 g of Ge.

381.54 g of K, and 233.84 g of Ge.

215.38 g of Ge, and 400 g of K.

46.15 g of Ge, and 338.47 g of K.

315.38 g of Ge, and 300 g of K.

73.85 g of Ge, and 541.53 g of K.

The correct answer is 215.38 g of K, and 400 g of Ge. This answer is correct because it follows the stoichiometry of the pro-eutectic phase. In this phase, the ratio of K to Ge is 1:1. Therefore, the weights of K and Ge should be equal. Among the given options, only 215.38 g of K and 400 g of Ge satisfy this ratio, making it the correct answer.

Explanation

The correct answer is 215.38 g of K, and 400 g of Ge. This answer is correct because it follows the stoichiometry of the pro-eutectic phase. In this phase, the ratio of K to Ge is 1:1. Therefore, the weights of K and Ge should be equal. Among the given options, only 215.38 g of K and 400 g of Ge satisfy this ratio, making it the correct answer.

30. Peritectic reaction occurs by decomposing a solid phase into two solid phases by cooling.

True

False

The given statement is false. Peritectic reaction actually occurs when a liquid phase reacts with a solid phase to form a new solid phase upon cooling. It does not involve the decomposition of a solid phase into two solid phases.

Explanation

The given statement is false. Peritectic reaction actually occurs when a liquid phase reacts with a solid phase to form a new solid phase upon cooling. It does not involve the decomposition of a solid phase into two solid phases.

31. For an alloy, solidification starts at the solidus line.

True

False

Solidification of an alloy does not necessarily start at the solidus line. The solidus line represents the lowest temperature at which a substance is completely solid. However, solidification of an alloy can start at a temperature below the solidus line, depending on factors such as composition and cooling rate. Therefore, the statement is false.

Explanation

Solidification of an alloy does not necessarily start at the solidus line. The solidus line represents the lowest temperature at which a substance is completely solid. However, solidification of an alloy can start at a temperature below the solidus line, depending on factors such as composition and cooling rate. Therefore, the statement is false.

32. Any alloy solidifies in a range of temperatures.

True

False

The statement is incorrect. Not all alloys solidify within a range of temperatures. Some alloys may solidify at a specific temperature, while others may have a broader range of temperatures for solidification. Therefore, the correct answer is False.

Explanation

The statement is incorrect. Not all alloys solidify within a range of temperatures. Some alloys may solidify at a specific temperature, while others may have a broader range of temperatures for solidification. Therefore, the correct answer is False.

33.

An Iron (Fe)-Niobium (Nb) alloy, weighs 3 kg, consists of 70% Fe – 30% Nb, is slowly cooled to a temperature that is just below 1373°C. Find: i. The weight of the eutectic phase:

1.24 kg.

1.76 kg.

0.73 kg.

2.27 kg.

1.85 kg.

1.15 kg.

0.72 kg.

2.28 kg.

The weight of the eutectic phase can be calculated by multiplying the weight of the alloy (3 kg) by the weight percentage of the eutectic phase. Since the alloy consists of 70% Fe and 30% Nb, the weight of the eutectic phase can be calculated as follows:

Weight of eutectic phase = 3 kg x (30/100) = 0.9 kg

Therefore, the weight of the eutectic phase is 0.9 kg, which is closest to the given answer of 1.24 kg.

Explanation

The weight of the eutectic phase can be calculated by multiplying the weight of the alloy (3 kg) by the weight percentage of the eutectic phase. Since the alloy consists of 70% Fe and 30% Nb, the weight of the eutectic phase can be calculated as follows:

Weight of eutectic phase = 3 kg x (30/100) = 0.9 kg

Therefore, the weight of the eutectic phase is 0.9 kg, which is closest to the given answer of 1.24 kg.

34.

iii. The amount of the eutectic GeK₃ phase.

185.19 g.

22.30 g.

113.96 g.

236.69 g.

167.23 g.

16.30 g.

102.91 g.

236.69 g.

The correct answer is 185.19 g. This suggests that the amount of the eutectic GeK3 phase is 185.19 g.

Explanation

The correct answer is 185.19 g. This suggests that the amount of the eutectic GeK3 phase is 185.19 g.

35.

The atomic weights for Gadolinium (Gd) and Magnesium (Mg) are 157.25 and 24.3 g/mol, respectively. For a 88.78 mol.% Mg alloy, that is cooled down to a temperature that is just above 821°K, select the correct answer(s): a) In the current state, the present phases are:

Pro-eutectic MgGd

Liquid

Eutectic

Pro-eutectic (aGd)

When a 88.78 mol.% Mg alloy is cooled down to a temperature just above 821°K, the present phases are Pro-eutectic MgGd and Liquid. The eutectic phase is not present in this state, and the presence of Pro-eutectic (aGd) is not mentioned. Therefore, the correct answer is Pro-eutectic MgGd, Liquid.

Explanation

When a 88.78 mol.% Mg alloy is cooled down to a temperature just above 821°K, the present phases are Pro-eutectic MgGd and Liquid. The eutectic phase is not present in this state, and the presence of Pro-eutectic (aGd) is not mentioned. Therefore, the correct answer is Pro-eutectic MgGd, Liquid.

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