Question

If 9.01 mol of CO occupies 44.9 L, what volume will 66.5 mol of CO occupy at the same temperature and pressure? Be sure your answer has the correct number of significant figures.

Answer 1

To find the volume that 66.5 mol of CO will occupy at the same temperature and pressure, we can use the concept of proportionality from the ideal gas law, which states that volume is directly proportional to the number of moles of gas when temperature and pressure are constant.

We can set up the ratio using the provided information:

\[
\frac{V_1}{n_1} = \frac{V_2}{n_2}
\]

Where:
- \( V_1 \) is the initial volume (44.9 L)
- \( n_1 \) is the initial number of moles (9.01 mol)
- \( V_2 \) is the final volume (unknown)
- \( n_2 \) is the final number of moles (66.5 mol)

Rearranging the equation to solve for \( V_2 \) gives:

\[
V_2 = V_1 \times \frac{n_2}{n_1}
\]

Substituting in the known values:

\[
V_2 = 44.9 \, \text{L} \times \frac{66.5 \, \text{mol}}{9.01 \, \text{mol}}
\]

Now we can calculate this:

\[
V_2 = 44.9 \, \text{L} \times 7.3776 \approx 331.33 \, \text{L}
\]

Now, we must consider significant figures. The initial values indicate that we should round to three significant figures because the least precise number (9.01 mol) has three significant figures.

Rounding \( 331.33 \, \text{L} \) to three significant figures gives:

\[
\boxed{331 \, \text{L}}
\]