Question

What mass of neon gas is required to fill a 5.00 -L container to a pressure of 1.02 atm at 25 'C ?

Short answer

4.20 grams of neon gas is required to fill the 5.00-L container at 1.02 atm and 25 °C.

Step-by-step solution

Convert temperature to Kelvin

To convert the temperature from Celsius to Kelvin, add 273.15: \(T(K) = T(°C) + 273.15\) \(T(K) = 25 + 273.15 = 298.15 K\)

Calculate the number of moles (n) using the Ideal Gas Law

Now, rearrange the ideal gas law equation to solve for the number of moles (n): \(n = \frac{PV}{RT}\) Plug in the given values: \(n = \frac{(1.02\,\text{atm})(5.00\,\text{L})}{(0.0821\,\text{L⋅atm/mol⋅K})(298.15\,\text{K})}\) \(n \approx 0.208\, \text{mol}\)

Calculate the mass of neon gas using molar mass of neon

The molar mass of neon is approximately 20.18 g/mol. To find the mass of neon gas required, multiply the number of moles by the molar mass: Mass = moles × molar mass Mass = \(0.208\, \text{mol} \times 20.18\, \text{g/mol}\) Mass = \(4.20\, \text{g}\) Therefore, 4.20 grams of neon gas is required to fill the 5.00-L container at 1.02 atm and 25 °C.

Key concepts

Moles Calculation

Understanding how to calculate moles is crucial when working with gases, such as neon, and using the Ideal Gas Law. The Ideal Gas Law equation is represented as \( PV = nRT \), where:

• \( P \) is the pressure of the gas
• \( V \) is the volume of the gas container
• \( n \) is the number of moles of the gas
• \( R \) is the ideal gas constant, \(0.0821\, \text{L}\cdot\text{atm/mol}\cdot\text{K}\)
• \( T \) is the temperature in Kelvin

The number of moles \( n \) represents the amount of substance present, and it is calculated by rearranging the equation to \( n = \frac{PV}{RT} \). This formula helps us determine how many moles of gas we have under specific conditions of pressure, volume, and temperature. For example, in the exercise, we determined there were approximately \( 0.208 \, \text{mol} \) of neon gas required in the container. This calculation is essential when determining the mass of gas required for any given conditions.

Temperature Conversion

Temperature conversion, particularly from Celsius to Kelvin, is a fundamental step in gas calculations because all temperature values in the Ideal Gas Law must be expressed in Kelvin. The conversion is straightforward:

• To convert Celsius to Kelvin, simply add \(273.15\)

Make sure you do this conversion accurately for precise calculations. In the given problem, the temperature was initially \(25\,°\text{C}\). By adding \(273.15\), this translates to \(298.15\,\text{K}\). Converting to Kelvin ensures that the temperature is on an absolute scale, which is essential for obeying the physical laws described by the Ideal Gas Law. It's important to always remember this step when dealing with gas law problems to avoid calculation errors.

Neon Gas Properties

Neon is a noble gas with some specific properties that affect its behavior in gas law calculations. As a monoatomic gas, its molar mass is relatively small, around \(20.18 \, \text{g/mol}\). Noble gases, like neon, are chemically inert due to their full valence electron shell, making them stable in pure form under most conditions.
When calculating the mass of neon gas needed in the exercise, the molar mass is used to convert the number of moles (\(n\)) to mass using the formula:

• Mass = moles \(\times\) molar mass

This property's understanding helps us determine that \(4.20 \, \text{g}\) of neon was necessary to fill the container to the specified conditions. These properties make neon an excellent choice for situations requiring an inert gas, such as in certain types of lighting and high-precision gas analysis.