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Chapter 15: Problem 92

How many moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) does it take to neutralize \(2.5\) moles of \(\mathrm{HNO}_{3}\) ?

Short Answer

Expert verified
It takes \(1.25\) moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) to neutralize \(2.5\) moles of \(\mathrm{HNO}_{3}\).

Step by step solution

01

Write the balanced chemical equation for the reaction

First, we need to write the chemical equation for the neutralization reaction between \(\mathrm{Ba}(\mathrm{OH})_{2}\) and \(\mathrm{HNO}_{3}\), and then balance it: \[\mathrm{Ba}(\mathrm{OH})_{2} + 2\mathrm{HNO}_{3} \rightarrow \mathrm{Ba}(\mathrm{NO}_{3})_{2} + 2\mathrm{H}_{2}\mathrm{O}\]
02

Determine the mole ratio of the reactants

Now that we have the balanced chemical equation, we can determine the mole ratio of the reactants. In this case, it is \(1:2\), meaning that for every mole of \(\mathrm{Ba}(\mathrm{OH})_{2}\), \(2\) moles of \(\mathrm{HNO}_{3}\) are required for complete neutralization.
03

Use the mole ratio to find the moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\)

Since we know the moles of \(\mathrm{HNO}_{3}\) and the mole ratio of the reactants, we can determine the moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) required to neutralize the given moles of \(\mathrm{HNO}_{3}\) using the following proportion: \[\frac{1 \, \text{mole} \, \mathrm{Ba}(\mathrm{OH})_{2}}{2 \, \text{moles} \, \mathrm{HNO}_{3}} = \frac{x \, \text{moles} \, \mathrm{Ba}(\mathrm{OH})_{2}}{2.5 \, \text{moles} \, \mathrm{HNO}_{3}}\]
04

Solve for x

Now we just need to solve for x to find the moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) needed: \(x = \frac{1 \, \text{mole} \, \mathrm{Ba}(\mathrm{OH})_{2} \times 2.5 \, \text{moles} \, \mathrm{HNO}_{3}}{2 \, \text{moles} \, \mathrm{HNO}_{3}}\) \(x = 1.25 \, \text{moles} \, \mathrm{Ba}(\mathrm{OH})_{2}\) Hence, it takes \(1.25\) moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) to neutralize \(2.5\) moles of \(\mathrm{HNO}_{3}\).

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Most popular questions from this chapter

If \(100 \mathrm{~mL}\) of an aqueous solution of nitric acid contains \(0.030\) mole of \(\mathrm{HNO}_{3}\), what is the \(\mathrm{pH}\) of the solution?

For each acid-base pair, write a balanced equation for the neutralization reaction: (a) Lithium hydroxide and hydroiodic acid (b) Acetic acid and sodium hydroxide (c) Hydrobromic acid and calcium hydroxide (d) Potassium hydroxide and phosphoric acid (assume all acidic protons react)

An ionic compound with the formula \(\operatorname{NaX}(\mathrm{X}\) is an unknown anion) is dissolved in water, and the resulting solution is basic. Is HX a strong acid or a weak acid? Explain.

Based solely on concentrations, when is an aqueous solution judged to be basic? Give two answers to this question.

\(\mathrm{HZ}\) is a weak acid. An aqueous solution of \(\mathrm{HZ}\) is prepared by dissolving \(0.020\) mol of \(\mathrm{HZ}\) in sufficient water to yield \(1.0 \mathrm{~L}\) of solution. The \(\mathrm{pH}\) of the solution was \(4.93\) at \(25.0{ }^{\circ} \mathrm{C}\). What is the \(K_{\mathrm{a}}\) of \(\mathrm{HZ}\) ?
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