A sample of ammonia (NH3) gas is completely decomposed to nitrogen and hydrogen over a heated iron catalyst. If the total pressure of the mixture of N2 and H2 is 1.80 atm, what is the partial pressure of N2? (LO 10.7) (a) 1.35 atm (b) 0.45 atm (c) 0.90 atm (d) 0.63 atm

Verified step by step guidance

1. Step 1: Write the balanced chemical equation for the decomposition of ammonia (NH_3) into nitrogen (N_2) and hydrogen (H_2). The balanced equation is: 2 NH_3(g) \rightarrow N_2(g) + 3 H_2(g).
2. Step 2: Use the stoichiometry of the balanced equation to determine the mole ratio between NH_3, N_2, and H_2. From the equation, 2 moles of NH_3 produce 1 mole of N_2 and 3 moles of H_2.
3. Step 3: Apply Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each component. Here, P_{total} = P_{N_2} + P_{H_2}.
4. Step 4: Use the mole ratio from Step 2 to express the partial pressures in terms of a single variable. Let x be the partial pressure of N_2. Then, the partial pressure of H_2 is 3x, because 3 moles of H_2 are produced for every mole of N_2.
5. Step 5: Substitute the expressions for partial pressures into the equation from Step 3: 1.80 atm = x + 3x. Solve for x to find the partial pressure of N_2.

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle allows us to calculate the pressure of a specific gas in a mixture by knowing the total pressure and the contributions of the other gases present.

Stoichiometry of Gas Reactions

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In the decomposition of ammonia (NH3) into nitrogen (N2) and hydrogen (H2), the balanced equation shows that two moles of NH3 produce one mole of N2 and three moles of H2, which is essential for determining the ratio of partial pressures in the resulting gas mixture.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates the pressure, volume, temperature, and number of moles of a gas. While this question primarily focuses on partial pressures, understanding the Ideal Gas Law helps in comprehending how gases behave under different conditions and can provide insights into the relationships between the gases involved in the reaction.