If 1.01 mol of CO occupies 14.8 L, how many moles of CO will occupy a 73.9 L container at the same temperature and pressure? Round your answer to 3 significant figures.

Answer 1

To find how many moles of CO will occupy a 73.9 L container at the same temperature and pressure, we can use the concept of molar volume.

From the given data, we know that:

• 1.01 mol of CO occupies 14.8 L.

We can first calculate the molar volume of CO: $$\text{Molar Volume}=\frac{\text{Number of moles}}{\text{Volume}}=\frac{1.01,\text{mol}}{14.8,\text{L}}\approx 0.068(\text{mol/L})$$

Now, we can use this molar volume to determine how many moles will occupy 73.9 L: $$\text{Number of moles}=\text{Volume}\times \text{Molar concentration}$$ $$\text{Number of moles}=\frac{73.9,\text{L}}{14.8,\text{L}}\times 1.01,\text{mol}\approx 5.01,\text{mol}$$

So, we need to know how many moles occupy 73.9 L, and that can also be calculated in a straightforward ratio since the temperature and pressure are constant.

Using the ratio of volumes: $$\text{Moles in 73.9 L}=1.01,\text{mol}\times \frac{73.9,\text{L}}{14.8,\text{L}}$$ Calculating this gives: $$\text{Moles in 73.9 L}\approx 1.01\times 4.99\approx 5.02,\text{mol}$$

Rounding to three significant figures, the answer is: $$\boxed{{\displaystyle 5.02}},\text{mol}$$