Calculate the energy (in kJ) needed to heat 75.3 g of butane from its liquid to gas phase without a change in temperature.

To calculate the answer, we need to know:

the temperature remains constant the butane boiling point of 0.0 °C
the butane heat of vaporization is 22.4 kJ/mol
the butane molar mass is 58.12 g/mol
Kelvin temperature = 273.15 + Celsius temperature

To calculate the energy needed to heat 75.3 g of butane from its liquid to gas phase at constant temperature (its boiling point), we use the following formula for phase change:

\[
q = n \times \Delta H_{\text{vap}}
\]

Where:
- \( q \) = energy required (in kJ),
- \( n \) = number of moles of butane,
- \( \Delta H_{\text{vap}} \) = heat of vaporization (22.4 kJ/mol).

### Step 1: Convert mass of butane to moles
We use the molar mass of butane to convert from grams to moles:

\[
n = \frac{75.3 \, \text{g}}{58.12 \, \text{g/mol}} = 1.296 \, \text{mol}
\]

### Step 2: Calculate the energy required
Now, we can calculate the energy using the heat of vaporization:

\[
q = 1.296 \, \text{mol} \times 22.4 \, \text{kJ/mol} = 29.03 \, \text{kJ}
\]

Thus, the energy required to vaporize 75.3 g of butane is approximately **29.03 kJ**.

Would you like further details or clarification on any steps?

### Related Questions:
1. How would the calculation change if the mass of butane were doubled?
2. What is the significance of the heat of vaporization in phase changes?
3. How is the heat of vaporization related to intermolecular forces in butane?
4. How does this calculation differ for substances other than butane?
5. Why does temperature remain constant during a phase change?

### Tip:
When dealing with phase changes, the temperature remains constant because the added energy is used to overcome intermolecular forces rather than increasing kinetic energy.

Calculate the energy (in kJ) needed to heat 75.3 g of butane from its liquid to gas phase without a change in temperature.

Learn how to calculate the energy needed to vaporize 75.3 g of butane using stoichiometric methods and phase change concepts. This problem involves calculating the moles of butane and using the heat of vaporization to determine energy. Suitable for high school students in Grades 10-12.

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