Final answer:
To find the number of moles of gas in a sample with known pressure, volume, and temperature, we use the ideal gas law. After converting the temperature from Celsius to Kelvin, the ideal gas law equation is applied and solved for the number of moles. The sample contains approximately 21.91 moles of gas.
Step-by-step explanation:
To calculate the number of moles of an ideal gas given its pressure, volume, and temperature, we can use the ideal gas law, which is PV = nRT. Here, P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹), and T is the temperature in Kelvin (K).
The ideal gas law needs the temperature in Kelvin, so the first step is to convert the given temperature from Celsius to Kelvin:
T = 50.11 °C + 273.15 = 323.26 K
Now, we substitute the given values into the ideal gas law:
(6.17 atm) × (92.13 L) = n × (0.0821 L·atm·K⁻¹·mol⁻¹) × (323.26 K)
To find n, we can rearrange the formula:
n = (6.17 atm × 92.13 L) / (0.0821 L·atm·K⁻¹·mol⁻¹ × 323.26 K)
By calculating the numerator and then dividing by the denominator, we get:
n ≈ 21.91 moles of gas.
Therefore, there are approximately 21.91 moles of gas in the sample.