Ideal Gas Law Calculation

A reaction requires 22.4 L of gas at STP. You have 25.0 L of gas at 101.5 kPa and 373 K. Which of the following statements is true? (Use the ideal gas law: PV = nRT where R = 8.31 L-kPa/mol-K.) The statement "You will have enough gas" is true. The ideal gas law provides a relationship between pressure (P), volume (V), temperature (T), and the number of moles of gas (n). Let's dive deeper into the calculation to understand why this statement is accurate.

Understanding Ideal Gas Law Calculation

The Ideal Gas Law: PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Gas constant (8.31 L-kPa/mol-K)
T = Temperature

Given data:
Volume (V) = 25.0 L
Pressure (P) = 101.5 kPa
Temperature (T) = 373 K

Calculating number of moles of gas (n) with the ideal gas law equation:

n = PV/RT

Substitute the values:

n = (101.5 kPa)(25.0 L) / (8.31 L-kPa/mol-K)(373 K)

n = 7.55 mol

The amount of gas we have is 7.55 mol, which is greater than the 4.89 mol needed for the reaction. Therefore, the statement "You will have enough gas" is accurate in this scenario.

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