Calculate the pressure (in atmospheres) of a gas at 298 K if it occupies 10.0 L and contains 0.50 moles of gas molecules.
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To calculate the pressure of a gas, we can use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Rearranging the equation to solve for P, we have: P = (nRT) / V.
Given that the volume (V) is 10.0 L, the number of moles (n) is 0.50 moles, the ideal gas constant (R) is 0.0821 L·atm/(mol·K), and the temperature (T) is 298 K, we can substitute these values into the equation:
P = (0.50 moles * 0.0821 L·atm/(mol·K) * 298 K) / 10.0 L
Simplifying this expression:
P = (12.71 L·atm) / 10.0 L
P = 1.271 atm
Therefore, the pressure of the gas is 1.271 atmospheres.
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