Constants for water
|$\Delta H _{\text {vap }}$ | $40.65 kJ / mol$ |
|---|---|
|$\Delta H _{ f }$ | $-285.83 kJ / mol$ |
|$\Delta H _{\text {fusion }}$ | $6.03 kJ / mol$ |
| specific heat | $4.186 J / g ^{\circ} C$ |
| molar mass | 18.02 g |
How much energy is consumed by thawing 4.3 g ice?
A. $4.3 g \times 1 mol / 18.02 g \times 40.65 kJ / mol$
B. $4.3 g \times 1 mol / 18.02 g \times 4.186 kJ / mol$
C. $4.3 g \times 1 mol / 18.02 g \times 6.03 kJ / mol$
D. $4.3 g \times 1 mol / 18.02 g \times(-285.83) kJ / mol$
Answer (2)
Convert the mass of ice to moles: moles = 18.02 g/mol 4.3 g = 0.2386 mol .
Calculate the energy required for thawing: energy = 0.2386 mol × 6.03 kJ/mol = 1.4389 kJ .
The energy consumed by thawing 4.3 g of ice is approximately 1.4389 kJ.
The correct option is C: 4.3 g × 18.02 g 1 mol × 6.03 kJ/mol .
Explanation
Problem Analysis and Given Data We are given the mass of ice (4.3 g) and asked to calculate the energy consumed when it thaws. Thawing is a phase transition from solid (ice) to liquid (water), and the energy required for this process is related to the enthalpy of fusion ( Δ H f u s i o n ). We are provided with the following:
Mass of ice = 4.3 g
Molar mass of water = 18.02 g/mol
Enthalpy of fusion, Δ H f u s i o n = 6.03 kJ/mol
Converting Mass to Moles First, we need to convert the mass of ice from grams to moles. We use the formula:
moles = molar mass mass
Substituting the given values:
moles of ice = 18.02 g/mol 4.3 g = 0.2386 mol
Calculating Energy Consumed Next, we calculate the energy required for thawing using the formula:
energy = moles × Δ H f u s i o n
Substituting the values we have:
energy = 0.2386 mol × 6.03 kJ/mol = 1.4389 kJ
Therefore, the energy consumed by thawing 4.3 g of ice is approximately 1.4389 kJ.
Matching with the Options Comparing our result with the given options, we can see that option C represents the correct calculation:
C. 4.3 g × 18.02 g 1 mol × 6.03 kJ/mol
This matches our step-by-step calculation.
Examples
Imagine you're making a refreshing glass of iced tea on a hot summer day. To figure out how much ice you need to cool down your tea, you need to know how much energy it takes to melt the ice. This problem demonstrates the calculation of the energy required to melt ice, which is crucial in many real-world applications, from making beverages to understanding climate processes. Knowing the enthalpy of fusion helps us determine the energy needed for phase transitions, allowing us to predict and control these processes effectively. For example, if you want to melt 4.3 g of ice, you'll need approximately 1.44 kJ of energy.
To thaw 4.3 g of ice, approximately 1.4389 kJ of energy is required, calculated using the enthalpy of fusion, which is 6.03 kJ/mol. Therefore, the correct option is C: 4.3 g × 18.02 g 1 mol × 6.03 kJ/mol .
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