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Chapter 4: Problem 77

A sample of limestone weighing \(1.005 \mathrm{~g}\) is dissolved in \(75.00 \mathrm{~mL}\) of \(0.2500 \mathrm{M}\) hydrochloric acid. The following reaction occurs: $$ \mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} $$ It is found that \(19.26 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{NaOH}\) is required to titrate the excess \(\mathrm{HCl}\) left after reaction with the limestone. What is the mass percent of \(\mathrm{CaCO}_{3}\) in the limestone?

Short Answer

Expert verified
Answer: The mass percent of calcium carbonate (CaCO3) in the limestone sample is 78.97%.

Step by step solution

01

Calculate moles of HCl initially present

We are given the initial volume and concentration of the HCl solution, so we can calculate the initial moles of HCl. The moles of HCl (initial) = Volume (L) × Concentration (M) Moles of HCl (initial) = 0.075 L × 0.2500 M = 0.01875 mol.
02

Calculate moles of NaOH used

We are given the volume and concentration of the NaOH solution, so we can calculate the moles of NaOH used. The moles of NaOH = Volume (L) × Concentration (M) Moles of NaOH = 0.01926 L × 0.150 M = 0.002889 mol.
03

Calculate moles of HCl reacted with NaOH

In an acid-base reaction, moles of the acid (HCl) and base (NaOH) interact at a 1:1 ratio. Hence, the moles of HCl reacted with NaOH are equal to the moles of NaOH used. Moles of HCl reacted with NaOH = 0.002889 mol.
04

Calculate moles of HCl reacted with CaCO3

To calculate the moles of HCl that reacted with the CaCO3, subtract the moles of HCl reacted with NaOH from the initial amount of HCl. Moles of HCl reacted with CaCO3 = Moles of HCl(initial) - Moles of HCl reacted with NaOH = 0.01875 - 0.002889 = 0.015861 mol
05

Calculate moles of CaCO3

Using the balanced chemical equation, we know that 1 mole of CaCO3 reacts with 2 moles of HCl. Hence, we can calculate the moles of CaCO3 present. Moles of CaCO3 = Moles of HCl reacted with CaCO3 / 2 = 0.015861 / 2 = 0.0079305 mol.
06

Calculate mass of CaCO3

To find the mass of CaCO3, multiply the moles by its molar mass (100.09 g/mol). Mass of CaCO3 = Moles of CaCO3 × Molar mass = 0.0079305 mol × 100.09 g/mol = 0.793194 g.
07

Calculate mass percent of CaCO3

Now, we can calculate the mass percent of CaCO3 in the limestone sample. Mass percent of CaCO3 = (Mass of CaCO3 / Total mass of sample) × 100 Mass percent of CaCO3 = (0.793194 g / 1.005 g) × 100 = 78.97 % (rounded to two decimal places).

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