Question

1 gram of a sample of \(\mathrm{CaCO}_{3}\) was strongly heated and the \(\mathrm{CO}_{2}\) liberated was absorbed in \(100 \mathrm{~mL}\) of \(0.5 \mathrm{M} \mathrm{NaOH}\) solution. Assuming \(90 \%\) purity for the sample. How many \(\mathrm{mL}\) of \(0.5 \mathrm{M}\) \(\mathrm{HCl}\) would be required to react with the resulting solution to reach the end point in presence of phenolphthalein? (a) \(73 \mathrm{~mL}\) (b) \(41 \mathrm{~mL}\) (c) \(82 \mathrm{~mL}\) (d) \(100 \mathrm{~mL}\) A sampla-a

Short answer

41 mL of 0.5 M HCl would be required to react with the resulting solution to reach the end point.

Step-by-step solution

Determine moles of CO2 absorbed in the NaOH solution

Given that 1 gram of a 90% pure sample of CaCO3 is heated, calculate the moles of pure CaCO3, which is 1 gram x 90%. Then use the molar mass of CaCO3 to convert this to moles. The balanced reaction is CaCO3 (s) -> CaO (s) + CO2 (g). Each mole of CaCO3 produces one mole of CO2.

Calculate moles of NaOH required to neutralize CO2

Use the stoichiometry of the reaction between CO2 and NaOH, which is CO2 (g) + 2 NaOH (aq) -> Na2CO3 (aq) + H2O (l), to calculate the moles of NaOH that reacted with the CO2 produced from the pure CaCO3.

Calculate remaining moles of NaOH

Given that 100 mL of 0.5 M NaOH solution was used initially, calculate the initial moles of NaOH. Then subtract the moles of NaOH that reacted with CO2 to find the remaining moles of unreacted NaOH.

Calculate moles of HCl required to neutralize remaining NaOH

Using the stoichiometry of the neutralization reaction NaOH (aq) + HCl (aq) -> NaCl (aq) + H2O (l), which is 1:1, determine the moles of HCl needed to react with the remaining NaOH.

Convert moles of HCl to volume of 0.5 M HCl solution

Use the molarity formula, moles = concentration x volume, to calculate the required volume of a 0.5 M HCl solution to neutralize the remaining NaOH.

Key concepts

Mole Concept

Understanding the mole concept is crucial in solving stoichiometry problems in physical chemistry. The mole allows chemists to count by weighing, as it is a unit that relates mass to the number of atoms, ions, or molecules in a substance. One mole is defined as the amount of substance containing the same number of discrete entities (such as atoms, molecules, or ions) as there are atoms in 12 grams of pure carbon-12. This number is known as Avogadro's number, which is approximately equal to \(6.022 \times 10^{23}\).

To calculate the moles of a substance, we use the formula: \(\text{moles} = \frac{\text{mass in grams}}{\text{molar mass}}\). For example, in the given exercise, the molar mass of \(\mathrm{CaCO_3}\) (calcium carbonate) is used to convert the mass of the pure sample into moles. This step is foundational in determining the amounts of reactants or products involved in a chemical reaction.

Neutralization Reactions

Neutralization reactions are a specific type of chemical reaction where an acid and a base react to form water and a salt. This process typically involves the transfer of protons from the acid to the base. A common example is the reaction between hydrochloric acid (\(\mathrm{HCl}\)) and sodium hydroxide (\(\mathrm{NaOH}\)), forming sodium chloride (\(\mathrm{NaCl}\)) and water (\(\mathrm{H_2O}\)).

In the context of our exercise, a neutralization reaction plays a key role when the liberated \(\mathrm{CO_2}\) reacts with \(\mathrm{NaOH}\) to form sodium carbonate (\(\mathrm{Na_2CO_3}\)) and water. Later, the remaining \(\mathrm{NaOH}\), which did not react with \(\mathrm{CO_2}\), is neutralized by \(\mathrm{HCl}\). These reactions are crucial to calculate the volume of \(\mathrm{HCl}\) needed to reach the endpoint in the titration, which is indicated by the phenolphthalein, a pH indicator that changes color at the endpoint.

Quantitative Analysis

Quantitative analysis in chemistry refers to the determination of the quantity or concentration of a substance within a mixture. In stoichiometry problems like the one in our exercise, quantitative analysis involves careful measurement and calculation to determine the exact amounts of reactants and products involved in a chemical reaction. For the titration performed in the exercise, quantitative analysis is used to calculate the volume of \(\mathrm{HCl}\) solution required to neutralize the remaining \(\mathrm{NaOH}\) in solution.

In this case, the stoichiometry of the reactions and the concept of molarity (moles of solute per liter of solution) are applied to find the volumes of the solutions. By using the formula \(\text{moles} = \text{concentration} \times \text{volume}\), and knowing the molarities and stoichiometry of the reactions, one can solve for the unknown volume. This way, students are able to predict the outcome of a quantitative experiment in the laboratory, such as a titration.