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A solution containing [tex]$1.15 \text{ mol}$[/tex] benzene dissolved in carbon tetrachloride has a concentration of [tex]0.86 \text{ m}[/tex]. How many kilograms of carbon tetrachloride must the solution contain?

Use molality [tex]=\frac{\text { moles of solute }}{\text { kilograms of solvent }}[/tex].

A. [tex]0.29 \text{ kg}[/tex]
B. [tex]0.75 \text{ kg}[/tex]
C. [tex]0.99 \text{ kg}[/tex]
D. [tex]1.3 \text{ kg}[/tex]



Answer :

GinnyAnswer
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]

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