How many milliliters of 0.105 M HCl are needed to titrate each of the following solutions to the equivalence point: (a) 45.0 mL of 0.0950 M NaOH? (c) 125.0 mL of a solution that contains 1.35 g of NaOH per liter?

검증된 단계별 안내

Step 1: Understand the concept of titration and equivalence point. In a titration, the equivalence point is reached when the amount of titrant added is stoichiometrically equivalent to the amount of substance present in the solution being titrated.

Step 2: For part (a), use the formula for titration: \( M_1V_1 = M_2V_2 \), where \( M_1 \) and \( V_1 \) are the molarity and volume of the HCl solution, and \( M_2 \) and \( V_2 \) are the molarity and volume of the NaOH solution. Substitute \( M_1 = 0.105 \) M, \( M_2 = 0.0950 \) M, and \( V_2 = 45.0 \) mL into the equation.

Step 3: Rearrange the equation to solve for \( V_1 \), the volume of HCl needed: \( V_1 = \frac{M_2V_2}{M_1} \). Substitute the known values into this equation to find \( V_1 \).

Step 4: For part (c), first calculate the molarity of the NaOH solution. Use the formula \( M = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)} \times \text{volume of solution (L)}} \). The molar mass of NaOH is approximately 40.00 g/mol. Calculate the molarity using 1.35 g/L.

Step 5: Once the molarity of NaOH is determined, use the titration formula \( M_1V_1 = M_2V_2 \) again, with \( M_1 = 0.105 \) M, \( M_2 \) as the calculated molarity of NaOH, and \( V_2 = 125.0 \) mL. Solve for \( V_1 \) to find the volume of HCl needed.

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주요 개념

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

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (a solution of known concentration) to a sample solution until the reaction reaches the equivalence point, where the amount of titrant equals the amount of substance in the sample. This process is often monitored using indicators or pH meters.

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for calculations in titration, as it allows for the determination of how much of a titrant is needed to react with a given volume of analyte. Understanding molarity is essential for converting between volumes and concentrations in titration problems.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relationships between the quantities of reactants and products in chemical reactions. In titration, stoichiometry is used to calculate the volume of titrant required based on the balanced chemical equation of the reaction. It allows for the determination of how much of one reactant is needed to completely react with a given amount of another reactant.