what volume does 2.5 moles of carbon monoxide occupy at 50.5 kPa pressure and 20.0 C?
To determine the volume of the gas, we can use the ideal gas law equation: PV = nRT.
Here's how you can solve it step by step:
1. Write down the given values:
- Pressure (P) = 50.5 kPa
- Number of moles (n) = 2.5 mol
- Universal Gas Constant (R) = 8.314 J/(mol·K) (you might need to convert the pressure and temperature units to match this constant)
- Temperature (T) = 20.0 °C = 20.0 + 273.15 K (Convert from Celsius to Kelvin by adding 273.15)
2. Convert the pressure unit from kPa to Pa:
- 50.5 kPa * 1000 Pa/kPa = 50,500 Pa
3. Convert the temperature from Celsius to Kelvin:
- 20.0 °C + 273.15 = 293.15 K
4. Plug the values into the ideal gas law equation:
- PV = nRT
- (50,500 Pa) * V = (2.5 mol) * (8.314 J/(mol·K)) * (293.15 K)
5. Solve for V (volume):
- V = (2.5 mol * 8.314 J/(mol·K) * 293.15 K) / 50,500 Pa
6. Multiply the values inside the parentheses:
- V = 611.1785 J/(K·Pa) / 50,500 Pa
7. Divide the two values to find the volume:
- V ≈ 0.0121 m³ or 12.1 L (rounded to 3 significant figures)
Therefore, 2.5 moles of carbon monoxide occupies approximately 0.0121 cubic meters or 12.1 liters at 50.5 kPa pressure and 20.0 °C temperature.