To determine the amount of heat absorbed when 25.00 moles of ice at [tex]\(0.0^\circ\text{C}\)[/tex] melts, we need to use the enthalpy of fusion ([tex]\(H_{\text{fus}}\)[/tex]) of water. Here's the detailed step-by-step method to find the solution:
1. Understand enthalpy of fusion ([tex]\(H_{\text{fus}}\)[/tex]):
- The enthalpy of fusion is the amount of heat required to convert one mole of a solid substance to a liquid at constant temperature and pressure. For water, [tex]\(H_{\text{fus}}\)[/tex] is given as [tex]\(6.011 \text{ kJ/mol}\)[/tex].
2. Given data:
- [tex]\(H_{\text{fus}} = 6.011 \text{ kJ/mol}\)[/tex]
- Number of moles of ice, [tex]\(n = 25.00\text{ moles}\)[/tex]
3. Heat absorbed calculation:
- The heat absorbed ([tex]\(q\)[/tex]) can be calculated using the formula:
[tex]\[
q = n \times H_{\text{fus}}
\][/tex]
- Substituting the given values:
[tex]\[
q = 25.00 \text{ moles} \times 6.011 \text{ kJ/mol}
\][/tex]
4. Perform the multiplication:
- Multiply the number of moles of ice by the enthalpy of fusion:
[tex]\[
q = 25.00 \times 6.011 = 150.275 \text{ kJ}
\][/tex]
Therefore, the amount of heat absorbed when 25.00 moles of ice at [tex]\(0.0^\circ\text{C}\)[/tex] melts is [tex]\(150.275 \text{ kJ}\)[/tex].
