Calculating Moles of Gas for an Ideal Gas Sample

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.