P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles, R is the gas constant (0.0821 L∙atm/(mol∙K)), and T is the temperature in Kelvins (K).
Using the ideal gas law, determine the pressure of a 0.820 mole sample of oxygen gas, under a temperature of 25.0 °C and a volume of 4.78 L.
To find the pressure using the ideal gas law formula \(PV = nRT\), we can rearrange the formula to solve for pressure \(P\):
\[ P = \dfrac{nRT}{V} \]
Given:
- n = 0.820 moles
- R = 0.0821 L∙atm/(mol∙K)
- T = 25.0 °C = 298.15 K
- V = 4.78 L
Plugging in the values, we get:
\[ P = \dfrac{(0.820 mol)(0.0821 L∙atm/(mol∙K))(298.15 K)}{4.78 L} \]
\[ P = \dfrac{21.467 L∙atm}{4.78 L} \]
\[ P = 4.49 atm \]
Therefore, the pressure of the 0.820 mole sample of oxygen gas under a temperature of 25.0 °C and a volume of 4.78 L is 4.49 atm.