125 g of dry ice (solid CO2) is dropped into a beaker containing 500 g of 66°C water. The dry ice converts directly to gas, leaving the solution.

When the dry ice is gone, the final temperature of the water is 29°C.

What is the heat of vaporization of solid CO2? (cwater = 1.00 cal/g⋅°C)

a. 37 cal/gb. 74 cal/gc. 111 cal/gd. 148 cal/g

The right option is (d).148 cal/g

Explanation:

Specific Latent Heat Of Vaporization: This is the quantity of heat required to change unit mass of a substance from either liquid to vapor, or solid to vapor without a change in temperature.

Heat gained by dry ice = Heat lost by the water

Q₁ = Q₂ ... equation 1

Where Q₁ = heat gained by the dry ice, Q₂ = heat lost by the water.

Q₁ = lm₁ ... equation 2

Q₂ = cm₂ΔT ... equation 3

Substituting the equation 1 into Equation 2,

lm₁ = cm₂ΔT ... equation 4

Where l = heat of vaporization of the dry ice, m₁ = mass of the dry ice, c = specific heat capacity of water, m₂ = mass of water, ΔT = change in temperature = T₁ - T₂

Making l the subject of formula in equation 4

l = cm₂ΔT/m₁ ... equation 5

Where c = 1.00 cal/g.°C, m₂ = 500g, ΔT = T₁ - T₂ = 66-29 = 37°C, m₁ = 125 g.

Substituting these values into equation 5

∴ l = (1 * 500 * 37) / 125

l = 148 cal/g

The right option is (d).148 cal/g