Question

What is the pressure in a 15.0 -L cylinder filled with 32.7 g of oxygen gas at a temperature of \(302 \mathrm{~K} ?\)

Short answer

To find the pressure, first calculate the number of moles of oxygen ( = \frac{32.7 g}{32.00 g/mol} = 1.0225 mol). Then apply the Ideal Gas Law to solve for P ( P = \frac{(1.0225 mol)(0.0821 L atm / K mol)(302 K)}{15.0 L} ). Calculate to get the pressure in atm.

Step-by-step solution

Convert the mass of oxygen gas to moles

First, we need to convert the mass of oxygen gas into moles using the molar mass of oxygen (O2). The molar mass of O2 is 32.00 g/mol. Use the formula: moles = mass (g) / molar mass (g/mol).

Apply the Ideal Gas Law

Use the Ideal Gas Law, which is written as PV = nRT. Where P is pressure, V is volume, n is number of moles, R is the ideal gas constant (0.0821 L atm / K mol), and T is temperature in Kelvin.

Solve for Pressure (P)

Rearrange the Ideal Gas Law to solve for P: P = (nRT) / V. Plug in the values for n (from Step 1), R, T, and V to solve for the pressure.

Key concepts

Gas Pressure

When discussing gases, one of the fundamental characteristics we consider is pressure. Gas pressure is the force that a gas exerts on the walls of its container and is a result of the frequent collisions of gas particles with the container walls.

This concept is extremely important when working with the Ideal Gas Law, as the law relates gas pressure (P) with volume (V), number of moles (n), and temperature (T) of the gas. In practical terms, increasing the number of gas particles (raising the moles of gas) or increasing the temperature can lead to an increase in pressure if the volume of the container remains constant.

Understanding how to measure and calculate pressure is essential in various scientific and engineering fields. Units of pressure include atmospheres (atm), pascals (Pa), and torr (among others), with the atmosphere being a common unit used in chemistry.

Moles Calculation

The mole is a fundamental unit in chemistry that quantifies the amount of substance. When working with gases, calculating moles is essential to relate the quantity of gas to its observable properties like pressure, volume, and temperature.

The number of moles of a substance is calculated by dividing the mass of the substance by its molar mass, which is the mass of one mole of that substance. For example, in the context of our exercise, the molar mass of oxygen, O₂, is 32.00 g/mol, so the number of moles of oxygen in a sample can be calculated using the formula: moles = \( \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).

This calculation is a crucial step in the Ideal Gas Law to find other properties of the gas. Additionally, understanding moles helps in stoichiometry, where chemists convert between mass, moles, and numbers of particles.

Molar Mass of Oxygen

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is a bridge between the macroscopic world (the amount we can feel or see) and the microscopic world of molecules and atoms.

The molar mass of a molecular compound like oxygen gas (O₂) is obtained by summing the molar masses of the individual atoms within the molecule. Oxygen has an atomic mass of approximately 16 g/mol, so the molar mass of an O₂ molecule is \(2 \times 16 \text{ g/mol} = 32 \text{ g/mol}\).

This molar mass is used when converting from grams to moles for the oxygen gas, which is the initial step in applying the Ideal Gas Law. Knowing the molar mass of a compound is a key concept in stoichiometry, allowing chemists to understand mass relationships in chemical reactions.