Sure, let's solve the problem step by step.
Step 1: Determine the number of moles of substance [tex]$X$[/tex].
Given:
- Mass of substance [tex]\(X\)[/tex] ([tex]\(m\)[/tex]) = 326.0 g
- Molar mass of substance [tex]\(X\)[/tex] ([tex]\(M\)[/tex]) = 58.45 g/mol
To find the number of moles ([tex]\(n\)[/tex]), we use the formula:
[tex]\[ n = \frac{m}{M} \][/tex]
Plug in the values:
[tex]\[ n = \frac{326.0 \, \text{g}}{58.45 \, \text{g/mol}} \][/tex]
This gives us:
[tex]\[ n \approx 5.577416595380667 \, \text{mol} \][/tex]
Step 2: Calculate the molar heat of fusion ([tex]\(\Delta H\)[/tex]).
Given:
- Heat released ([tex]\(q\)[/tex]) = 4325.8 cal
- Number of moles ([tex]\(n\)[/tex]) = 5.577416595380667 mol
To find the molar heat of fusion ([tex]\(\Delta H\)[/tex]), we use the relationship:
[tex]\[ q = n \Delta H \][/tex]
Rearrange to solve for [tex]\(\Delta H\)[/tex]:
[tex]\[ \Delta H = \frac{q}{n} \][/tex]
Plug in the values:
[tex]\[ \Delta H = \frac{4325.8 \, \text{cal}}{5.577416595380667 \, \text{mol}} \][/tex]
This gives us:
[tex]\[ \Delta H \approx 775.592055214724 \, \text{cal/mol} \][/tex]
Step 3: Choose the correct option.
The molar heat of fusion is approximately [tex]\( 775.6 \, \text{cal/mol} \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{775.6 \, \text{cal/mol}} \][/tex]
