Given that the specific heat capacities of ice and steam are 2.06 J/g degrees celsius, respectively, and considering the information about water given in exercise 16, calculate the total quantity of heat evolved when 10.0g of steam at 200. degrees celsius is condensed, cooled, and frozen to ice at -50 degrees celsius
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To calculate the total quantity of heat evolved when steam is condensed, cooled, and frozen to ice, we need to consider the heat changes at each step.
Step 1: Condensing steam to water
To condense steam to water, we need to calculate the heat transferred during the phase change using the equation:
q = m * ΔHv
Given:
Specific heat capacity of steam (Cv) = 2.06 J/g°C
Mass of steam (m) = 10.0g
Change in temperature (ΔT) = (100 - 200) = -100°C (heat loss during condensation)
Latent heat of vaporization (ΔHv) = 40.7 J/g
Calculating the heat transferred during condensation:
q1 = m * ΔHv = 10.0g * 40.7 J/g = 407 J
Step 2: Cooling water from 100°C to 0°C
To cool the water from 100°C to 0°C, we need to calculate the heat transferred using the equation:
q = m * C
Given:
Specific heat capacity of water (C) = 4.18 J/g°C
Change in temperature (ΔT) = (0 - 100) = -100°C (heat loss during cooling)
Mass of water (m) = 10.0g
Calculating the heat transferred during cooling:
q2 = m * C * ΔT = 10.0g * 4.18 J/g°C * (-100°C) = -4180 J
Step 3: Freezing water to ice
To freeze water to ice, we need to calculate the heat transferred during the phase change using the equation:
q = m * ΔHf
Given:
Specific heat capacity of ice (Cf) = 2.06 J/g°C
Change in temperature (ΔT) = (-50 - 0) = -50°C (heat loss during freezing)
Latent heat of fusion (ΔHf) = 334 J/g
Mass of ice (m) = 10.0g
Calculating the heat transferred during freezing:
q3 = m * ΔHf = 10.0g * 334 J/g = 3340 J
Now, to find the total quantity of heat evolved:
Total heat evolved = q1 + q2 + q3 = 407 J + (-4180 J) + 3340 J = -433 J
(Note: The negative sign indicates the heat is being released, or evolved.)
Therefore, the total quantity of heat evolved when 10.0g of steam at 200. degrees celsius is condensed, cooled, and frozen to ice at -50 degrees celsius is approximately -433 J.