What is the pressure in a 19.0-L cylinder filled with 34.3 g of oxygen gas at a temperature of 312 K?

Verified step by step guidance

1. Identify the relevant variables from the problem: volume (V) = 19.0 L, mass of oxygen gas (m) = 34.3 g, temperature (T) = 312 K.
2. Calculate the number of moles of oxygen gas (n) using the molar mass of oxygen (O2), which is approximately 32.00 g/mol. Use the formula: n = m / molar mass.
3. Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L\(\cdot\)atm/mol\(\cdot\)K), and T is the temperature in Kelvin.
4. Substitute the values for n, V, R, and T into the ideal gas law equation to solve for P (pressure).
5. Ensure that all units are consistent (e.g., volume in liters, temperature in Kelvin, pressure in atm) when performing calculations.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the pressure of a gas when the other variables are known.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For oxygen (O2), the molar mass is approximately 32.00 g/mol. Understanding molar mass is essential for converting grams of a substance to moles, which is necessary for using the Ideal Gas Law effectively.

Gas Constant (R)

The gas constant (R) is a proportionality constant in the Ideal Gas Law that relates the energy scale to the temperature scale. Its value is typically 0.0821 L·atm/(K·mol) when pressure is measured in atmospheres and volume in liters. Knowing the correct value of R is crucial for accurate calculations involving gas behavior under various conditions.