To determine the size of a container required to hold 10 moles of an ideal gas at standard temperature and pressure (STP), we can use the ideal gas law, which is given by the formula:
\[ PV = nRT \]
Where:
- \( P \) = pressure (in pascals)
- \( V \) = volume (in cubic meters)
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant (approximately \( 8.314 , \text{J/(mol K)} \))
- \( T \) = temperature (in kelvin)
Given:
- \( P = 1.013 \times 10^5 , \text{Pa} \) (1 ATM)
- \( n = 10 , \text{moles} \)
- \( R = 8.314 , \text{J/(mol K)} \)
- \( T = 273 , \text{K} \)
Rearranging the ideal gas law to solve for volume \( V \):
\[ V = \frac{nRT}{P} \]
Now substituting in the values:
\[ V = \frac{10 , \text{moles} \times 8.314 , \text{J/(mol K)} \times 273 , \text{K}}{1.013 \times 10^5 , \text{Pa}} \]
Calculating the numerator:
\[ 10 \times 8.314 \times 273 \approx 22700.56 , \text{J} \]
Now substituting the values back into the equation:
\[ V \approx \frac{22700.56 , \text{J}}{1.013 \times 10^5 , \text{Pa}} \]
Calculating this:
\[ V \approx 0.224 , \text{m}^3 \]
Thus, to hold 10 moles of an ideal gas at standard temperature and pressure (STP), you would need a container that has a volume of approximately 0.224 cubic meters, which is equivalent to about 224 liters.