How is the [tex]$\Delta H_{\text {vap }}$[/tex] used to calculate the mass of liquid boiled by 1 kJ of energy?
A. [tex]$1 kJ \times \Delta H_{\text {vap }} \times g / mol \text{ liquid}$[/tex]
B. [tex]$1 kJ \times 1 / \Delta H_{\text {vap }} \times g / mol$[/tex] liquid
C. [tex]$1 kJ \times 1 / \Delta H_{\text {vap }} \times mol / g$[/tex] liquid
D. [tex]$1 kJ \times \Delta H_{\text {vap }} \times mol / g$[/tex] liquid
Answer (2)
The problem requires finding the mass of liquid boiled by 1 kJ of energy using Δ H vap .
Recognize that Δ H vap is in kJ/mol, so 1/Δ H vap has units of mol/kJ.
Multiply 1 kJ by 1/Δ H vap to find the number of moles vaporized.
Multiply the number of moles by the molar mass (g/mol) to find the mass: 1 kJ × Δ H vap 1 × mol g . The final answer is 1 kJ × 1/Δ H vap × g / m o l .
Explanation
Understanding the Problem We are asked to find the correct formula for calculating the mass of liquid boiled by 1 kJ of energy, using the heat of vaporization, Δ H vap . The heat of vaporization represents the amount of energy (usually in kJ) needed to vaporize one mole of a liquid. The options give different ways to combine 1 kJ, Δ H vap , and the molar mass (g/mol) to find the mass of the boiled liquid.
Finding the Number of Moles The heat of vaporization, Δ H vap , is typically given in units of kJ/mol. This means that to find the number of moles that can be vaporized by 1 kJ of energy, we need to divide 1 kJ by Δ H vap . This gives us: Δ H vap (kJ/mol) 1 kJ = Δ H vap 1 mol .
Calculating the Mass Now that we have the number of moles, we need to convert it to mass using the molar mass, which is given in g/mol. To do this, we multiply the number of moles by the molar mass: Mass = Moles × Molar Mass = Δ H vap 1 mol × mol g = Δ H vap 1 × mol g kJ .So the correct formula is: 1 kJ × Δ H vap 1 × mol g .
Final Answer Comparing our derived formula with the given options, we see that option B matches our result: 1 kJ × Δ H vap 1 × mol g .Therefore, the correct answer is B.
Examples
Imagine you're heating water to make steam for a steam engine. The Δ H vap tells you how much energy you need to turn one mole of water into steam. If you know how much energy your heater provides (say, 1 kJ), you can calculate how many grams of water you can boil with that energy. This is crucial for designing efficient steam engines or any process involving phase changes, like distillation or refrigeration. By understanding the relationship between energy input, heat of vaporization, and mass, engineers can optimize these systems for maximum performance and energy efficiency.
To calculate the mass of liquid boiled by 1 kJ using \text{0}8}{\text{vap}}, divide 1 kJ by \text{0}8}{\text{vap}} to find moles, then multiply by molar mass to find mass. The correct formula is therefore: 1 \text{ kJ} \times \frac{1}{ \text{0}8}{\text{vap}} \times \frac{\text{g}}{\text{mol}} . The chosen option is B.
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