Question

Calculate the amount of energy in Joules required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point. The m_p, b_p, and specific heat of mercury are -39^degree C, - 375^degree C, and 0.140 J/g^degree C, respectively. Compare with the amount of heat needed to change 10 g of ice at 0^degree C to steam at 100^degree C.

Answer 1

The amount of energy required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point is -1641 J, while the amount of heat needed to change 10 g of ice at 0°C to steam at 100°C is 7833.5 J.

Step-by-step explanation:

To calculate the amount of energy required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point, we need to consider the energy required to heat the solid mercury from its melting point to its boiling point, and then the energy required for the phase change from solid to liquid, and from liquid to vapor.

First, we calculate the energy required to heat the solid mercury:

1. Calculate the temperature change: -375°C - (-39°C) = -336°C
2. Calculate the energy using the specific heat equation: Q = m × c × ΔT, where m is the mass, c is the specific heat, and ΔT is the temperature change.
3. Q = 10 g × 0.140 J/g°C × -336°C = -4704 J

Next, we calculate the energy required for the phase change:

1. For the solid to liquid phase change, we use the latent heat of fusion, which is 11.3 J/g.
2. Q = m × ΔH, where m is the mass and ΔH is the latent heat of fusion.
3. Q = 10 g × 11.3 J/g = 113 J

For the liquid to vapor phase change, we use the latent heat of vaporization, which is 295 J/g.

1. Q = m × ΔH, where m is the mass and ΔH is the latent heat of vaporization.
2. Q = 10 g × 295 J/g = 2950 J

Finally, we add up the energies for each step to get the total energy required:

Total energy = -4704 J + 113 J + 2950 J = -1641 J

The amount of heat required to change 10 g of ice at 0°C to steam at 100°C can be calculated in a similar way, by considering the energy required to heat the ice from 0°C to its melting point, the energy for the phase change from ice to water, and the energy to heat the water from its boiling point to 100°C. The specific heat of ice is 2.09 J/g°C, the latent heat of fusion is 334 J/g, and the latent heat of vaporization is 2260 J/g.

Using the same steps as before, we calculate:

1. Energy to heat ice from 0°C to its melting point:
   1. Temperature change: 0°C - (-15°C) = 15°C
   2. Energy = 10 g × 2.09 J/g°C × 15°C = 313.5 J
2. Energy for the phase change from ice to water:
   1. Energy = 10 g × 334 J/g = 3340 J
3. Energy to heat water from its boiling point to 100°C:
   1. Temperature change: 100°C - 0°C = 100°C
   2. Energy = 10 g × 4.18 J/g°C × 100°C = 4180 J

Total energy = 313.5 J + 3340 J + 4180 J = 7833.5 J

Therefore, the amount of energy required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point is -1641 J, while the amount of heat needed to change 10 g of ice at 0°C to steam at 100°C is 7833.5 J.

Answer 2

Q: Calculate the amount of energy in Joules required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point. The m_p, b_p, and specific heat of mercury are -39^degree C, 375^degree C, and 0.140 J/g^degree C, respectively. Compare with the amount of heat needed to change 10 g of ice at 0^degree C to steam at 100^degree C.

Answer:

The heat required = 575.4 J

Q₂ > Q₁ (The amount of energy required by the mercury is small than the amount of energy required by the water.)

Step-by-step explanation:

Q₁ = c₁m₁(T₂-T₁)....................... Equation 1

Where Q₁ = amount of heat or Energy. c₁ = specific heat capacity of mercury, m₁ = mass of mercury, T₂ = Temperature of mercury at boiling point, T₁ = Temperature of mercury at melting point.

Given: m₁ = 10 g , c₁ = 0.14 J/g.°C, T₂ = 372 °C, T₁ = -39 °C

Substituting these values into equation 1

Q₁ = 10×0.14 (372+39)

Q₁ = 1.4(411)

Q₁ = 575.4 J.

Thus the heat required = 575.4 J

Q₂ = c₂m₂(θ₂-θ₁)....................... Equation 2

Where Q₂ = heat required to change the temperature of water from 0 °C to 100 °C, c₂ = specific heat capacity of water, m₂ = mass of water, θ₂ = Final temperature of water, θ₁ = Initial Temperature of water.

Given: m₁ = 10 g, θ₂ = 100 °C, θ₁ = 0 °C

Constant: c₂ = 4.2 J/g.°C

Substituting these values into equation 2

Q₂ = 10(4.2)(100-0)

Q₂ = 4200 J.

Comparing Q₁ and Q₂,

Q₂ > Q₁

Hence the amount of energy required by the mercury is small than the amount of energy required by the water.