A current of 11.3 A is applied to 1.25 L of a solution of 0.552 M HBr converting some of the H⁺ to H₂(g), which bubles out of solution. What is the pH of the solution after 73 minutes?

검증된 단계별 안내

Determine the initial moles of HBr in the solution using the formula: \( \text{moles} = \text{molarity} \times \text{volume} \).

Calculate the total charge passed through the solution using the formula: \( Q = I \times t \), where \( I \) is the current in amperes and \( t \) is the time in seconds.

Use Faraday's laws of electrolysis to find the moles of \( H^+ \) converted to \( H_2 \) gas. The number of moles of electrons is equal to \( \frac{Q}{F} \), where \( F \) is Faraday's constant (96485 C/mol).

Subtract the moles of \( H^+ \) converted to \( H_2 \) from the initial moles of \( H^+ \) to find the remaining moles of \( H^+ \) in the solution.

Calculate the new concentration of \( H^+ \) ions and use the formula \( \text{pH} = -\log[H^+] \) to find the pH of the solution.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Electrolysis

Electrolysis is a chemical process that uses an electric current to drive a non-spontaneous reaction. In this context, the current applied to the HBr solution causes the reduction of H+ ions to form hydrogen gas (H2), which escapes as bubbles. Understanding electrolysis is crucial for determining how much H+ is converted and how it affects the solution's pH.

Molarity and Stoichiometry

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. In this problem, the initial concentration of HBr is 0.552 M, which helps calculate the number of moles of H+ present. Stoichiometry allows us to relate the amount of H+ converted to H2 gas during electrolysis, which is essential for determining the change in pH.

pH Calculation

pH is a logarithmic scale used to specify the acidity or basicity of a solution, calculated as pH = -log[H+]. As H+ ions are converted to H2 gas, the concentration of H+ decreases, leading to an increase in pH. Understanding how to calculate pH based on changes in H+ concentration is vital for solving the problem.

A current of 11.3 A is applied to 1.25 L of a solution of 0.552 M HBr converting some of the H+ to H2(g), which bubles out of solution. What is the pH of the solution after 73 minutes?