To determine the mass of NaCl that releases 452 kJ of heat as it changes into a liquid, let's go through the step-by-step solution.
### Step 1: Identify the given values
1. Enthalpy change of fusion [tex]\(\Delta H_{\text{fus}}\)[/tex]: [tex]\(30.2 \, \text{kJ/mol}\)[/tex]
2. Enthalpy change of vaporization [tex]\(\Delta H_{\text{vap}}\)[/tex]: [tex]\(171 \, \text{kJ/mol}\)[/tex]
3. Total heat released [tex]\(q\)[/tex]: [tex]\(452 \, \text{kJ}\)[/tex]
### Step 2: Calculate the total enthalpy change for the entire process
The total enthalpy change for the entire process is the sum of the enthalpy changes of fusion and vaporization:
[tex]\[
\Delta H_{\text{total}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}
\][/tex]
Substitute the given values:
[tex]\[
\Delta H_{\text{total}} = 30.2 \, \text{kJ/mol} + 171 \, \text{kJ/mol} = 201.2 \, \text{kJ/mol}
\][/tex]
### Step 3: Use the relation [tex]\( q = n \Delta H \)[/tex] to find the number of moles ([tex]\( n \)[/tex])
Rearrange the equation to solve for [tex]\( n \)[/tex]:
[tex]\[
n = \frac{q}{\Delta H_{\text{total}}}
\][/tex]
Substitute the given heat ([tex]\( q \)[/tex]) and the total enthalpy change:
[tex]\[
n = \frac{452 \, \text{kJ}}{201.2 \, \text{kJ/mol}} \approx 2.2465 \, \text{mol}
\][/tex]
### Step 4: Calculate the molar mass of NaCl
The molar mass of NaCl (sodium chloride) is:
[tex]\[
\text{Molar mass of NaCl} = 58.44 \, \text{g/mol}
\][/tex]
### Step 5: Calculate the mass of NaCl
Use the number of moles [tex]\( n \)[/tex] to find the mass:
[tex]\[
\text{Mass of NaCl} = n \times \text{Molar mass of NaCl}
\][/tex]
Substitute the number of moles and molar mass:
[tex]\[
\text{Mass of NaCl} = 2.2465 \, \text{mol} \times 58.44 \, \text{g/mol} \approx 131.29 \, \text{g}
\][/tex]
### Step 6: Compare the result with the given options
Given options are: 2.64 g, 22.1 g, 155 g, 875 g.
Among these values, the closest to our calculated mass of 131.29 g is:
155 g
Therefore, the mass of NaCl that releases 452 kJ of heat as it changes into a liquid is:
[tex]\[
\boxed{155 \, \text{g}}
\][/tex]
