Question

At what temperature will a 1.0 -g sample of neon gas exert a pressure of 500 . torr in a 5.0 -L container?

Short answer

The temperature at which a 1.0-g sample of neon gas exerts a pressure of 500 torr in a 5.0-L container is approximately 203.16 Kelvin.

Step-by-step solution

Convert mass to moles

To calculate the number of moles (n) of neon gas, we will use its molar mass. The molar mass of neon (Ne) is approximately 20.18 g/mol. n = (mass of Ne) / (molar mass of Ne) = (1.0 g) / (20.18 g/mol) = 0.0496 mol

Convert pressure from torr to atm

Since we will be using the Ideal Gas Law formula where R (Ideal Gas Constant) is in units of atm·L/mol·K, we need to convert the pressure from torr to atm. 1 atm = 760 torr P (atm) = (500 torr) × (1 atm / 760 torr) = 0.6579 atm

Apply Ideal Gas Law formula

Now that we have the pressure in atm, the volume in liters, and the number of moles of neon, we can solve for the temperature using the Ideal Gas Law formula, PV = nRT. We will be using R = 0.0821 atm·L/mol·K. 0.6579 atm × 5.0 L = 0.0496 mol × 0.0821 atm·L/mol·K × T

Solve for temperature T

To find the temperature T, we need to isolate T in the equation: (0.6579 atm × 5.0 L) / (0.0496 mol × 0.0821 atm·L/mol·K) = T T = 203.16 K Therefore, the temperature at which a 1.0-g sample of neon gas exerts a pressure of 500 torr in a 5.0-L container is approximately 203.16 Kelvin.

Key concepts

Understanding Molar Mass

Molar mass is a property that relates the mass of a substance to the number of its particles, more specifically, moles. In the context of an Ideal Gas Law problem, knowing the molar mass of a gas, such as neon, is pivotal. This value is typically found on the periodic table and is expressed in grams per mole (g/mol).

When given the mass of a gas, the molar mass allows you to convert that mass into moles—a necessary step for using the Ideal Gas Law. For neon, its molar mass is approximately 20.18 g/mol, meaning that each mole of neon weighs 20.18 grams. To convert grams to moles, you would divide the mass of the gas by its molar mass. This foundational step enables further calculations concerning gas behavior under various conditions.

Converting Pressure Units

Pressure is a measure of force exerted per unit area and it is commonly measured in units such as atmospheres (atm), torr, or pascals (Pa). In many science problems, particularly when dealing with the Ideal Gas Law, it is necessary to convert pressure units for consistency and compatibility with the gas constant (R).

In our example, we convert pressure from torr to atm, with the understanding that 1 atm equals 760 torr. By using the conversion factor (1 atm / 760 torr), we can easily convert any pressure value given in torr to atm. This allows for smooth substitution into the Ideal Gas Law and prevents any potential unit discrepancies that could invalidate the solution.

Temperature Calculation with the Ideal Gas Law

Temperature plays a critical role in understanding gas behavior and is an integral component of the Ideal Gas Law, which is given by the equation PV = nRT. Here, T stands for temperature and must be measured in Kelvin (K) for the equation to work accurately as Kelvin is the SI unit for temperature.

To isolate and solve for temperature in the Ideal Gas Law equation, you rearrange it to T = (PV)/(nR). By calculating the pressure in atmospheres, volume in liters, the number of moles, and using the appropriate value for R, one can straightforwardly determine the temperature. Always remember, when performing your final calculation, make sure that all units are correctly converted and applied so that the resulting temperature is accurate.