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·Kâ»Â¹Â·molâ»Â¹), 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) à (92.13 L) = n à (0.0821 L·atm·Kâ»Â¹Â·molâ»Â¹) à (323.26 K)
To find n, we can rearrange the formula:
n = (6.17 atm à 92.13 L) / (0.0821 L·atm·Kâ»Â¹Â·molâ»Â¹ à 323.26 K)
By calculating the numerator and then dividing by the denominator, we get:
n â 21.91 moles of gas.
Therefore, there are approximately 21.91 moles of gas in the sample.