Question

If 9.65 moles of an ideal gas has a pressure of 4.77 atm, and a volume of 43.85 L, what is the temperature of the sample?

Answer 1

If 9.65 moles of an ideal gas has a pressure of 4.77 atm, and a volume of 43.85 L, what is the temperature of the sample?

Solution:

The ideal gas law is:

$$pV = nRT$$

where P is the absolute pressure of the gas, V is the volume of the gas, n is the amount of substance of gas (measured in moles), T is the absolute temperature of the gas and R is the ideal, or universal, gas constant. From this equation:

$$T = \frac{pV}{nR}$$ $$\begin{array}{l} p \text{ (Pa)} = 4.77 \times 101325 = 483320.25 \\ V \text{ (m}^3\text{)} = 43.85 / 1000 = 4.385 \times 10^{-2} \\ T \text{ (K)} = (483320.25 \times 4.385 \times 10^{-2}) / (9.65 \times 8.314) = 264.16 \\ \end{array}$$

Answer: 264.16 K