Find the mass of barium metal (in grams) that must react with O₂ to produce enough barium oxide to prepare 1.0 L of a 0.10 M solution of OH^-.

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Write the balanced chemical equation for the reaction: 2Ba + O_2 \(\rightarrow\) 2BaO.

Determine the moles of OH^- needed: Use the formula \(\text{Molarity}\) = \(\frac{\text{moles of solute}\)}{\(\text{volume of solution in liters}\)} to find the moles of OH^- required for 1.0 L of a 0.10 M solution.

Relate moles of OH^- to moles of BaO: Since BaO reacts with water to form Ba(OH)_2, and each BaO produces two OH^-, calculate the moles of BaO needed.

Relate moles of BaO to moles of Ba: From the balanced equation, 1 mole of BaO is produced from 1 mole of Ba.

Calculate the mass of Ba: Use the molar mass of Ba to convert moles of Ba to grams.

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주요 개념

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

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this case, stoichiometry will help us find the mass of barium needed to produce a specific amount of barium oxide, which is essential for preparing the desired concentration of hydroxide ions.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for understanding how to prepare solutions with specific concentrations. In this question, knowing that we need a 0.10 M solution of OH- allows us to calculate the number of moles of hydroxide ions required, which directly relates to the amount of barium oxide produced.

Chemical Reactions and Products

Understanding the chemical reaction between barium and oxygen is essential for this problem. Barium reacts with oxygen to form barium oxide (BaO), and this reaction must be balanced to determine the stoichiometric coefficients. The formation of hydroxide ions from barium oxide in solution is also important, as it connects the mass of barium needed to the final concentration of hydroxide ions in the solution.

Find the mass of barium metal (in grams) that must react with O2 to produce enough barium oxide to prepare 1.0 L of a 0.10 M solution of OH-.