Question

A gaseous mixture contains 6.25 g of He and 4.97 g of Ne. What volume does the mixture occupy at STP? Calculate the partial pressure of each gas in the mixture at STP.

Short answer

The volume of the gas mixture at STP is \(47.26 L\), with the partial pressures of helium and neon being 0.8639 atm and 0.1361 atm, respectively.

Step-by-step solution

Calculate the moles of each gas in the mixture

To find the moles of each gas, we will use their respective molar masses: Molar mass of He = 4.00 g/mol Molar mass of Ne = 20.18 g/mol Now divide the given mass of each gas by its molar mass: Moles of He = 6.25 g / 4.00 g/mol = 1.5625 mol Moles of Ne = 4.97 g / 20.18 g/mol = 0.24625 mol

Use the ideal gas law to find the total volume at STP

The ideal gas law is given by: PV = nRT At STP (Standard Temperature and Pressure), the temperature T = 273.15 K, and the pressure P = 1 atm. The total moles of gas in the mixture are the sum of the moles of He and Ne. Total moles (n_total) = moles of He + moles of Ne = 1.5625 mol + 0.24625 mol = 1.80875 mol Using the ideal gas law, solve for V (volume): V = n_total * R * T / P We know that the ideal gas constant R = 0.0821 L atm / (mol K). Now we simply plug in the values: V = (1.80875 mol) * (0.0821 L atm / (mol K)) * (273.15 K) / (1 atm) = \(47.26 L\)

Calculate the mole fractions of He and Ne

The mole fraction of a gas is the ratio of the moles of that gas to the total moles of the mixture. We will first calculate the mole fractions of He and Ne respectively: Mole fraction of He (X_He) = moles of He / total moles = 1.5625 mol / 1.80875 mol = 0.8639 Mole fraction of Ne (X_Ne) = moles of Ne / total moles = 0.24625 mol / 1.80875 mol = 0.1361

Calculate the partial pressures of He and Ne at STP

Finally, we will calculate the partial pressures of He and Ne using their mole fractions and the total pressure (P_total) at STP: Partial pressure of He (P_He) = X_He * P_total = 0.8639 * 1 atm = 0.8639 atm Partial pressure of Ne (P_Ne) = X_Ne * P_total = 0.1361 * 1 atm = 0.1361 atm The volume of the gas mixture at STP is \(47.26 L\) and the partial pressures of He and Ne are 0.8639 atm and 0.1361 atm, respectively.

Key concepts

Stoichiometry

Stoichiometry is like the mathematical toolkit for chemists. It helps in understanding the relationships between reactants and products in chemical reactions. Essentially, it allows us to calculate the amounts (in moles, grams, or even liters of gases) needed or produced in a chemical reaction.

In the exercise mentioned, stoichiometry helps determine the number of moles of each gas in the mixture. By identifying how many moles of helium (He) and neon (Ne) are present, we derive essential values for further calculations. This involves using the molar masses of the gases, found in periodic tables, to convert given mass into moles.

Using stoichiometry in gas calculations ensures accuracy in predicting how different substances will behave under the same conditions. It's like having a precise recipe for a successful chemical reaction.

Mole Fraction

The mole fraction is a way to describe the concentration of a component in a mixture. It's calculated by dividing the number of moles of one component by the total number of moles in the mixture.

For example, in a gas mixture containing helium and neon, we find the mole fractions by dividing the moles of each gas by the total moles in the mixture.

In formula terms, the mole fraction of helium (X_{He}) can be calculated as \( X_{He} = \frac{\text{moles of He}}{\text{total moles}} \). Likewise, the mole fraction of neon (X_{Ne}) is \( X_{Ne} = \frac{\text{moles of Ne}}{\text{total moles}} \).

Mole fraction is crucial because it helps us understand how much of each substance makes up the mixture, regardless of how much total substance is present.

Partial Pressure Calculation

Partial pressure refers to the pressure exerted by an individual gas in a mixture of gases. To find the partial pressure, we use the mole fraction of the gas and multiply it by the total pressure of the mixture.

In the context of the exercise, at Standard Temperature and Pressure (STP), we calculate the partial pressure of helium as \( P_{He} = X_{He} \cdot P_{\text{total}} \) and for neon as \( P_{Ne} = X_{Ne} \cdot P_{\text{total}} \).

Knowing each gas's partial pressure helps predict how it will behave in the mixture, as gases in a mixture act independently. Hence, understanding partial pressures ensures accurate insights into the study of gas behaviors and reactions.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry to ensure experiments are standardized and comparisons are fair.

STP conditions are defined as a temperature of 273.15 K (0°C) and a pressure of 1 atm. Under these conditions, gases exhibit predictable behaviors according to the Ideal Gas Law, making calculations straightforward.

Using STP allows us to calculate properties like volume and pressure of gas mixtures under standard conditions, ensuring consistent and replicable results across various experiments.

Gas Mixtures

Gas mixtures are composed of two or more different gases that occupy the same physical space but don't chemically react with each other. Each gas in a mixture behaves independently, contributing to the overall characteristics of the mixture.

In solving the exercise, understanding that helium and neon form a gas mixture is important. Though they intermingle, they maintain their own individual pressures and volumes, described mathematically by the Ideal Gas Law and Dalton's Law of Partial Pressures.

Gas mixtures like the one described give an excellent opportunity to apply the Ideal Gas Law and calculate meaningful values like total volume at STP and partial pressures, providing deeper insight into the nature of gaseous compounds.