**Educational Content: Understanding Pressure and Mole Fraction in a Nitrogen Mixture**1. **What fraction of the pressure is due to nitrogen?** *Note:* The fraction due to nitrogen is calculated using the formula: \[ \text{fraction due to nitrogen} = \frac{\text{N}_2 \text{ pressure}}{\text{total pressure}} = \frac{P_{N_2}}{P_T} \]2. **What is the nitrogen mole fraction in the tank?** *Note:* The mole fraction of nitrogen is determined by: \[ \text{mole fraction of nitrogen} = \frac{\text{moles of N}_2}{\text{total moles}} = \frac{n_{N_2}}{n_T} \]3. **What is the relationship between the nitrogen pressure ratio in Key Question 4 and the nitrogen mole fraction in Key Question 5?** Express this relationship in the form of an equation.This educational content explains how to determine the fraction of pressure and mole fraction in a gas mixture, specifically nitrogen, using fundamental equations in chemistry. **Model: Gases Exert Pressure Independently**This educational table illustrates how gases exert pressure independently under a controlled environment.| Condition | Pressure | Volume | Temperature | Comment ||-----------|----------|--------|-------------|---------|| Initial | 1.0 atm | 22.4 L | 273 K | 1.0 mole of N₂ gas fills the tank. || Final | 3.0 atm | 22.4 L | 273 K | 2.0 moles of O₂ gas have been added to the 1 mole of N₂ gas in the tank. |**Explanation:**- **Initial Condition:** At the start, the tank contains 1.0 mole of nitrogen gas (N₂) at a pressure of 1.0 atm, a volume of 22.4 liters, and a temperature of 273 K.- **Final Condition:** After modifications, the pressure increases to 3.0 atm while keeping the volume and temperature constant. This change results from adding 2.0 moles of oxygen gas (O₂) to the existing nitrogen gas in the tank. This example demonstrates the concept of partial pressures and how gases in a mixture contribute independently to the total pressure.

Given: At constant temperature and volume of 273 K and 22.4 L respectively, the pressure of the tank increases from 1.0 atm to 3.0 upon adding 2.0 moles of O2 to 1.0 mole of N2.Initially, the number of moles of N2 present in the tank is 1 mole. 2 moles of O2 are added to this tank containing N2 gas. The pressure when only N2 was present is 1.0 atm thus, the pressure due to N2 is 1.0 atm. On adding O2, the pressure increases to 3.0 atm such that total pressure=3.0 atm Thus, the fraction of pressure due to nitrogen is calculated as: Pfr (N2)=Pressure due to N2Total Pressure =PN2PT =1.0 atm3.0 atm =13 Number of moles of N2= 1 mol Number of moles of O2=2 mol Total number of moles, nT=nN2+nO2 =1.0+2.0 mol =3.0 mol Thus, the mol fraction of N2, χN2 is calculated as: χN2=nN2nT =13The nitrogen pressure ratio is equal to the nitrogen mol fraction that is, equal to, 1/3 which concludes, pN2pT=nN2nTpN2=nN2nT×pTpN2=χN2×pT that is, the partial pressure of a gas is equal to the product of the mol fraction of that gas and the total pressure.

Science

Chemistry

What fraction of the pressure is due to nitrogen? Note: fraction due to nitrogen = N₂ pressure/total pressure = PN₂ / PT What is the nitrogen mole fraction in the tank? Note: mole fraction of nitrogen = moles of N₂ / total moles = = N₂/nT hat is the relationship between the nitrogen pressure ratio in Key Question 4 and the nitrogen ole fraction in Key Question 5? Express this relationship in the form of an equation.

What fraction of the pressure is due to nitrogen? Note: fraction due to nitrogen = N₂ pressure/total pressure = PN₂ / PT What is the nitrogen mole fraction in the tank? Note: mole fraction of nitrogen = moles of N₂ / total moles = = N₂/nT hat is the relationship between the nitrogen pressure ratio in Key Question 4 and the nitrogen ole fraction in Key Question 5? Express this relationship in the form of an equation.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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