To find the pressure of the gas given the number of moles, temperature, and volume, we can use the Ideal Gas Law, which is stated as:
\[ PV = nRT \]
where
\[ P \] = pressure of the gas
\[ V \] = volume of the container
\[ n \] = number of moles of the gas
\[ R \] = ideal gas constant
\[ T \] = temperature in Kelvin
Let's use the given variables to solve for the pressure \( P \).
1. Number of moles of carbon monoxide (\( n \)): 6.50 moles
2. Volume of the container (\( V \)): 31.8 L (since the ideal gas constant we will be using is in liters, we don't need to convert this to any other unit)
3. Temperature in Celsius (\( T_{C} \)): 54.0 °C, which needs to be converted to Kelvin.
The conversion formula for Celsius to Kelvin is:
\[ T_{K} = T_{C} + 273.15 \]
So,
\[ T_{K} = 54.0 + 273.15 = 327.15 \text{ K} \]
The value for the ideal gas constant \( R \) depends on the units used for pressure. A commonly used value for \( R \) is 0.0821 L·atm/(mol·K) when the pressure is in atmospheres (atm).
Now we can solve for the pressure \( P \).
Rearrange the Ideal Gas Law to solve for \( P \):
\[ P = \frac{nRT}{V} \]
Plug in the values:
\[ P = \frac{6.50 \text{ moles} \times 0.0821 \frac{\text{L·atm}}{\text{mol·K}} \times 327.15 \text{ K}}{31.8 \text{ L}} \]
Once we calculate this, we will have the pressure in atmospheres, which then we can round to three significant digits as required.
\[ P = \frac{6.50 \times 0.0821 \times 327.15}{31.8} \]
\[ P = \frac{174.96525}{31.8} \]
\[ P \approx 5.499 \text{ atm} \]
The pressure of the gas, rounded to three significant digits, is approximately 5.50 atm.
