Questions: Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 × 10^4 mmHg and -23°C.

Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 × 10^4 mmHg and -23°C.
Transcript text: 5. Ex: Calculate the volume occupied by 637 g of $\mathrm{SO}_{2}(\mathrm{MM} 64.07)$ at $6.08 \times 10^{4} \mathrm{mmHg}$ and $-23^{\circ} \mathrm{C}$.
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Solution

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Solution Steps

Step 1: Convert Mass to Moles

First, calculate the number of moles of \(\mathrm{SO}_2\) using its molar mass.

\[ \text{Moles of } \mathrm{SO}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{637 \, \text{g}}{64.07 \, \text{g/mol}} = 9.940 \, \text{mol} \]

Step 2: Convert Temperature to Kelvin

Convert the temperature from Celsius to Kelvin.

\[ T = -23^\circ \mathrm{C} + 273.15 = 250.15 \, \text{K} \]

Step 3: Convert Pressure to Atmospheres

Convert the pressure from mmHg to atmospheres.

\[ P = \frac{6.08 \times 10^4 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 80.00 \, \text{atm} \]

Step 4: Use the Ideal Gas Law to Find Volume

Use the ideal gas law \(PV = nRT\) to find the volume \(V\).

  • \(P = 80.00 \, \text{atm}\)
  • \(n = 9.940 \, \text{mol}\)
  • \(R = 0.0821 \, \text{L atm/mol K}\)
  • \(T = 250.15 \, \text{K}\)

\[ V = \frac{nRT}{P} = \frac{9.940 \times 0.0821 \times 250.15}{80.00} = 2.553 \, \text{L} \]

Final Answer

The volume occupied by 637 g of \(\mathrm{SO}_2\) is \(\boxed{2.553 \, \text{L}}\).

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