To determine the number of kilograms of carbon tetrachloride (CCl\(_4\)) required for the solution, we will use the formula for molality:
[tex]\[
\text{molality (m)} = \frac{\text{moles of solute}}{\text{kilograms of solvent}}
\][/tex]
Given data:
- Moles of solute (benzene) = 1.15 moles
- Molality (m) = 0.86 mol/kg
We need to find the kilograms of solvent (carbon tetrachloride, CCl\(_4\)). We can rearrange the formula to solve for kilograms of solvent:
[tex]\[
\text{kilograms of solvent} = \frac{\text{moles of solute}}{\text{molality}}
\][/tex]
Plugging in the values:
[tex]\[
\text{kilograms of solvent} = \frac{1.15 \text{ moles}}{0.86 \text{ mol/kg}}
\][/tex]
[tex]\[
\text{kilograms of solvent} \approx 1.3372093023255813 \text{ kg}
\][/tex]
Given the options:
- 0.29 kg
- 0.75 kg
- 0.99 kg
- 1.3 kg
The closest option to our calculated value (1.3372093023255813 kg) is 1.3 kg.
Therefore, the number of kilograms of carbon tetrachloride in the solution is approximately:
[tex]\[
\boxed{1.3 \text{ kg}}
\][/tex]
