How many moles of an ideal gas are present in a 50.6 L sample at 35 ° C and 875 torr?

Question

Quizplus · Accepted Answer

To find the number of moles of an ideal gas, we can use the ideal gas law equation: PV = nRT. First, we need to ensure all units are in the correct format for the constants we are using. The volume is given in liters, which is fine for our purposes. The temperature needs to be converted from Celsius to Kelvin (K = °C + 273.15), so 35 °C = 308.15 K. The pressure needs to be converted from torr to atm because the R constant we'll use is typically defined with pressure in atmospheres: 1 atm = 760 torr, so 875 torr = 875 / 760 atm. The R constant is 0.0821 L·atm/(mol·K).$$ P = 875 \, \text{torr} = \frac{875}{760} \, \text{atm} $$$$ V = 50.6 \, \text{L} $$$$ T = 35 \, \text{°C} = 308.15 \, \text{K} $$$$ R = 0.0821 \, \text{L·atm/(mol·K)} $$Rearranging the ideal gas law to solve for n (number of moles):$$ n = \frac{PV}{RT} $$$$ n = \frac{(875/760) \times 50.6}{0.0821 \times 308.15} $$$$ n \approx 2.30 \, \text{mol} $$Therefore, the correct answer is 2.30 mol, which corresponds to choice B.

How Many Moles of an Ideal Gas Are Present in a 50.6