(a) How many milliliters of 0.120 M HCl are needed to completely neutralize 50.0 mL of 0.101 M Ba(OH)₂ solution?

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Step 1: Write down the balanced chemical equation for the reaction. In this case, the reaction is between hydrochloric acid (HCl) and barium hydroxide (Ba(OH)2). The balanced equation is: 2HCl + Ba(OH)2 -> BaCl2 + 2H2O

Step 2: Calculate the moles of Ba(OH)2 in the solution using the formula: moles = volume (in liters) x molarity. In this case, the volume of Ba(OH)2 solution is 50.0 mL or 0.050 L and the molarity is 0.101 M.

Step 3: From the balanced chemical equation, we can see that the stoichiometric ratio between HCl and Ba(OH)2 is 2:1. This means that for every mole of Ba(OH)2, we need 2 moles of HCl to neutralize it. So, multiply the moles of Ba(OH)2 by 2 to get the moles of HCl needed.

Step 4: Now, calculate the volume of HCl solution needed using the formula: volume (in liters) = moles / molarity. In this case, the molarity of HCl is 0.120 M. Convert the volume from liters to milliliters by multiplying by 1000.

Step 5: The result is the volume of 0.120 M HCl needed to completely neutralize the 50.0 mL of 0.101 M Ba(OH)2 solution.

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Key Concepts

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

Neutralization Reaction

A neutralization reaction occurs when an acid reacts with a base to produce water and a salt. In this case, hydrochloric acid (HCl) reacts with barium hydroxide (Ba(OH)2). The balanced chemical equation helps determine the stoichiometric relationships between the reactants, which is essential for calculating the volumes needed for complete neutralization.

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). In this question, the molarity of HCl and Ba(OH)2 solutions is crucial for determining how much of each solution is required for the reaction, as it allows for the conversion between volume and the amount of substance.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the proportions of substances consumed and produced. In this scenario, stoichiometry is used to relate the moles of HCl needed to neutralize the moles of Ba(OH)2 present in the solution, facilitating the calculation of the required volume of HCl.