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Chapter 12: Problem 14

In a titration, \(16.02 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) was required to titrate \(0.2011 \mathrm{~g}\) of an unknown acid, \(\mathrm{HX}\). What is the molar mass of the acid?

Short Answer

Expert verified
The molar mass of the acid HX is 180.25 g/mol.

Step by step solution

01

Calculate moles of NaOH used

To find the moles of NaOH used in the titration, multiply the volume of the NaOH solution (in liters) by its concentration in molarity (moles per liter).
02

Write the balanced chemical equation

Assume a 1:1 mole ratio between NaOH and HX for the reaction, as no additional information is given. The equation is: NaOH(aq) + HX(aq) -> NaX(aq) + H2O(l).
03

Determine moles of HX reacted

Using the stoichiometric ratio from the balanced equation, calculate the moles of HX that reacted with the NaOH.
04

Calculate molar mass of HX

Calculate the molar mass by dividing the mass of HX used by the number of moles of HX reacted.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a measure of the concentration of a solution, indicating how many moles of a solute are present in a liter of solution. It is denoted as M and is calculated using the formula:
\[ M = \frac{moles \text{ of solute} }{volume \text{ of solution in liters} } \]
In the context of titration, molarity helps us understand the concentration of the titrant, which is the solution of known concentration used to determine the unknown concentration of a substance. In our exercise, we are dealing with a given concentration of NaOH (0.100 M), which allows us to find the moles of NaOH used by multiplying this molarity by the volume of NaOH solution in liters.
Stoichiometry
Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In our exercise, stoichiometry is used to relate the moles of NaOH to the moles of the unknown acid, HX, based on the balanced chemical equation. The mole ratio is derived from the coefficients of the reactants and products in the balanced equation. If the ratio is 1:1, it means one mole of NaOH reacts with one mole of HX. Understanding stoichiometry is essential as it allows us to convert between moles of different substances in a reaction.
Balanced Chemical Equation
A balanced chemical equation is a representation of a chemical reaction where the number of atoms for each element is the same on both sides of the equation, respecting the law of conservation of mass. In our exercise, the balanced chemical equation is assumed to be NaOH (aq) + HX (aq) -> NaX (aq) + H2O (l), with a 1:1 mole ratio between NaOH and HX. The balanced equation is central to the concept of stoichiometry, as it provides the ratio of the reactants and products, which is used to calculate the amount of substances that have reacted.
Molar Mass
Molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It is calculated by summing the atomic weights of the atoms in the compound's molecular formula. The molar mass is vital for converting between grams and moles of a substance. In our titration problem, we calculate the molar mass of HX by dividing the mass of HX used in the experiment by the moles of HX that reacted, which were stoichiometrically equivalent to the moles of NaOH used.

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Most popular questions from this chapter

When a hydrocarbon burns, water is produced as well as carbon dioxide. (For this reason, clouds of condensed water droplets are often seen coming from automobile exhausts, especially on a cold day.) The density of gasoline is \(0.79 \mathrm{~g} \cdot \mathrm{mL}^{-1}\). Assume gasoline to be represented by octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), for which the combustion reaction is $$ \begin{aligned} 2 \mathrm{C}_{\mathrm{g}} \mathrm{H}_{18}(\mathrm{l}) &+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \\ & 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \end{aligned} $$ Calculate the mass of water produced from the combustion of \(1.0 \mathrm{~L}\) of gasoline.

Impure phosphoric acid for use in the manufacture of fertilizers is produced by the reaction of sulfuric acid on phosphate rock, of which a principal component is \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)\). The reaction is $$ \begin{aligned} \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{~s}) &+3 \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow \\ & 3 \mathrm{CaSO}_{4}(\mathrm{~s})+2 \mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq}) \end{aligned} $$ (a) How many moles of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) can be produced from the reaction of \(200 \mathrm{~kg}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ? (b) Determine the mass of calcium sulfate that is produced as a by. product of the reaction of \(200 \mathrm{~mol} \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\).

A vitamin C tablet was analyzed to detcrmine whether it did in fact contain, as the manufacturer claimed, \(1.0 \mathrm{~g}\) of the vitamin. A tablet was dissolved in water to form a \(100.00-\mathrm{mL}\). solution, and a \(10.0-\mathrm{mL}\). sample was titrated with iodine (as potassium triiodide). It required \(10.1 \mathrm{~mL}\) of \(0.0521 \mathrm{MI}_{3}\) (aq) to reach the stoichiometric point in the titration, Given that \(1 \mathrm{~mol} \mathrm{I}_{3}^{-}-1 \mathrm{~mol}\) vitamin \(\mathrm{C}\) in the reaction, is the manufacturer's claim correct? The molar mass of vitamin \(\mathrm{C}\) is \(176 \mathrm{~g} \cdot \mathrm{mol}^{-1}\).

A 15.00-mL. sample of sodium hydroxide was titrated to the stoichiometric point with \(17.40 \mathrm{~mL}\). of \(0.234 \mathrm{M} \mathrm{HCl}(\mathrm{aq})\). (a) What is the initial molarity of \(\mathrm{NaOH}\) in the solution? (b) Calculate the mass of \(\mathrm{NaOH}\) in the solution.

Potassium superoxide, \(\mathrm{KO}_{2}\), is utilized in closedsystem breathing apparatus to remove carbon dioxide and water from exhaled air. The removal of water generates oxygen for breathing by the reaction $$ 4 \mathrm{KO}_{2}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{~g})+4 \mathrm{KOH}(\mathrm{s}) $$ The potassium hydroxide removes carbon dioxide from the apparatus by the reaction $$ \mathrm{KOH}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{KHCO}_{3}(\mathrm{~s}) $$ (a) What mass of potassium superoxide generates \(20.0 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ? (b) What mass of \(\mathrm{CO}_{2}\) can be removed from the apparatus by \(100 \mathrm{~g}\) of \(\mathrm{KO}_{2}\) ?
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