Final answer:
To determine the number of moles of gas in a 45.0 L container at 25°C and 500 mmHg, the Ideal Gas Law is used after converting pressure to atmospheres and temperature to Kelvin. The calculation reveals there are approximately 1.191 moles of gas in the container.
Step-by-step explanation:
The student asked how many moles of gas are in a 45.0 L container at 25°C and 500 mmHg. To find the number of moles, we can use the Ideal Gas Law, which is PV = nRT. In this equation, P stands for pressure, V stands for volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin.
First, we must convert the given conditions to appropriate units for the gas constant (R = 0.0821 L·atm·K-1·mol-1). The pressure needs to be converted to atmospheres (1 atm = 760 mmHg), and the temperature to Kelvin (K = °C + 273.15). So we have:
- Pressure (P) = 500 mmHg * (1 atm / 760 mmHg) = 0.6579 atm
- Volume (V) = 45.0 L
- Temperature (T) = 25 °C + 273.15 = 298.15 K
Using these values in the Ideal Gas Law:
n = PV / RT = (0.6579 atm * 45.0 L) / (0.0821 L·atm·K-1·mol-1 * 298.15 K) = 1.191 mol
Therefore, there are approximately 1.191 moles of gas in the 45.0 L container at 25°C and 500 mmHg.