Ch.10 - Gases

Problem 61a2

Chapter 10, Problem 61a2

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, what is the partial pressure of N2 after mixing?

Verified step by step guidance

Step 1: Identify the initial conditions for each gas. For He: Volume (V1) = 1.5 L, Pressure (P1) = 1.0 atm, Temperature (T) = 26°C. For Ar: Volume (V2) = 2.5 L, Pressure (P2) = 1.5 atm, Temperature (T) = 26°C.

Step 2: Calculate the total volume after the valve is opened. Total Volume (V_total) = V1 + V2 = 1.5 L + 2.5 L.

Step 3: Use the ideal gas law to find the number of moles of N2 in each container before mixing. For He: n1 = (P1 * V1) / (R * T). For Ar: n2 = (P2 * V2) / (R * T).

Step 4: Calculate the total number of moles of N2 after mixing. Total moles (n_total) = n1 + n2.

Step 5: Use the ideal gas law to find the partial pressure of N2 after mixing. P_total = (n_total * R * T) / V_total.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Partial Pressure

Partial pressure is the pressure exerted by a single gas in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. This concept is crucial for determining the behavior of gases when they are allowed to mix, as it helps in calculating the contribution of each gas to the overall pressure.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law assumes that gases behave ideally, meaning they occupy no volume and have no intermolecular forces. Understanding this law is essential for solving problems involving gas mixtures, as it allows for the calculation of changes in pressure and volume when gases are combined.

Gas Mixture Calculations

When dealing with gas mixtures, it is important to apply the principles of gas laws to determine the final conditions after mixing. This involves calculating the total volume and using the initial pressures and volumes of the individual gases to find their new partial pressures. These calculations are fundamental in predicting how gases will behave when they are allowed to mix in a closed system.

Recommended video:

Guided course

03:51

Gas Stoichiometry Calculation Example

Related Practice

Textbook Question

During a person's typical breathing cycle, the CO2 concentration in the expired air rises to a peak of 4.6% by volume. (a) Calculate the partial pressure of the CO2 in the expired air at its peak, assuming 1 atm pressure and a body temperature of 37 °C.

1360

views

Textbook Question

Acetylene gas, C2H21g2, can be prepared by the reaction of calcium carbide with water: CaC21s2 + 2 H2O1l2¡Ca1OH221aq2 + C2H21g2 Calculate the volume of C2H2 that is collected over water at 23 °C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 100.4 kPa. (The vapor pressure of water is tabulated in Appendix B.)

988

views

Textbook Question

Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, how does the volume occupied by the N2 gas change?

683

views

Textbook Question

Consider a mixture of two gases, A and B, confined in a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A?

834

views

Open Question

A mixture containing 0.50 mol H2(g), 1.00 mol O2(g), and 3.50 mol N2(g) is confined in a 25.0-L vessel at 25 °C. Calculate the partial pressure of H2, O2, and N2.

Open Question

A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 °C.