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In \(20 \mathrm{~mL}\) of a solution of \(\mathrm{HCl}, 3 \mathrm{~g}\) of \(\mathrm{CaCO}_{3}\) were dissolved, \(0.5 \mathrm{~g}\) of \(\mathrm{CaCO}_{3}\) being left undissolved. Find out the strength of this solution in terms of (i) normality and (ii) \(g / \mathrm{L}\). Find the volume of this acid which would be required to make 1 litre of normal solution of this acid.

Short Answer

Expert verified
The strength of HCl is 2.5 N and 91.25 g/L. 400 mL of solution makes 1 L of 1 N solution.

Step by step solution

01

Write the Reaction Equation

The reaction between hydrochloric acid (HCl) and calcium carbonate (\(\text{CaCO}_3\)) can be described by the chemical equation:\[\text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2\]This equation shows that one mole of \(\text{CaCO}_3\) reacts with two moles of HCl.
02

Calculate the Moles of Calcium Carbonate

We know that the initial mass of \(\text{CaCO}_3\) is \(3\,\text{g}\) and \(0.5\,\text{g}\) remains undissolved. Hence, the mass of \(\text{CaCO}_3\) that reacted is \(3 - 0.5 = 2.5\,\text{g}\).\[\text{Molar mass of } \text{CaCO}_3 = 100\,\text{g/mol}\]Therefore, the number of moles of \(\text{CaCO}_3\) that reacted is \[\frac{2.5}{100} = 0.025\,\text{mol}\]
03

Determine the Moles of HCl Used

According to the reaction equation, 1 mole of \(\text{CaCO}_3\) reacts with 2 moles of HCl. Therefore, 0.025 moles of \(\text{CaCO}_3\) will need \(2 \times 0.025 = 0.05\,\text{mol}\) of HCl.
04

Calculate the Normality of the HCl Solution

Normality (N) is defined as the number of equivalents of solute per liter of solution. Since HCl is a monoprotic acid, its normality equals its molarity. The volume of the HCl solution is \(20\,\text{mL} = 0.02\,\text{L}\).\[\text{Normality} = \frac{0.05}{0.02} = 2.5\,\text{N}\]
05

Calculate Strength in g/L

To calculate the strength of the HCl solution in \(g/L\), use the formula: \[\text{Strength} = \text{Normality} \times \text{Equivalent weight of HCl}\]. The equivalent weight of HCl is \(36.5\,\text{g/mol}\).\[\text{Strength} = 2.5 \times 36.5 = 91.25\, \text{g/L}\]
06

Calculate Volume for 1 Liter of Normal Solution

To determine the volume of the 2.5 N solution required to make 1 liter of a 1 N solution, use the dilution equation \(N_1V_1 = N_2V_2\). Where \(N_1 = 2.5\,\text{N}\), \(V_1\) is the volume we need to find, \(N_2 = 1\,\text{N}\), and \(V_2 = 1\,\text{L}\).\[2.5 \cdot V_1 = 1 \cdot 1\]Solving for \(V_1\), \[V_1 = \frac{1}{2.5} = 0.4\,\text{L} = 400\,\text{mL}\]

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Key Concepts

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

Molecular reactions
Chemical reactions involve the transformation of reactants into products, often resulting in the formation of new substances with different properties. In the case of the reaction between hydrochloric acid (HCl) and calcium carbonate (CaCO鈧), the process is an example of a molecular reaction. Here, the chemical equation \[ \text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{H}_2\text{O} + \text{CO}_2 \] represents the interchange of atoms, resulting in the formation of calcium chloride (CaCl鈧), water (H鈧侽), and carbon dioxide (CO鈧). Understanding the balance of this equation is crucial. - It tells us how much of each substance is needed or produced. - Each molecule of CaCO鈧 reacts with two molecules of HCl. - This stoichiometry is essential for predicting the amounts of reactants needed or products formed in a reaction.
Molarity calculations
Molarity (M) represents the concentration of a solution, indicating moles of solute per liter of solution. In this problem, the challenge is to understand how molarity links with normality, especially since HCl is a monoprotic acid. When determining normality, - It matches molarity because each HCl molecule can donate one proton (H鈦). - Here, moles of HCl required for the reaction is calculated by stoichiometry, matching the moles of CaCO鈧 reacting times two. - With this, the normality is simply achieved by dividing moles of HCl by the total volume of solution in liters, simplifying our concentration calculation. Ensure you adjust volume into liters (i.e., 20 ml is 0.02 l) for accurate normality results.
Chemical equations analysis
Analyzing chemical equations involves more than just balancing numbers. It requires a deeper dive into what these numbers represent. In the provided scenario, each component of the chemical equation must be scrutinized: - **Reactants and Products**: Understand which substances begin and what are formed. CaCO鈧 and HCl yield CaCl鈧, H鈧侽, and CO鈧. - **Stoichiometry Importance**: The equation shows specific relationships; for instance, one mole of CaCO鈧 reacts completely with two moles of HCl. - **Practical Implications**: This informs us about how the leftover material (e.g., 0.5 g CaCO鈧 in this case) affects the calculation of reacted moles. - **Reactions in Solution**: Here, the focus also shifts from solids to the concentration and volume of solutions. Proper interpretation of such equations enables us to predict reaction yields and compare with experimental results, providing insights into reaction efficiencies and potential side reactions.

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Most popular questions from this chapter

\(1.0 \mathrm{~g}\) carbonate of a metal was dissolved in \(50 \mathrm{~mL} \mathrm{~N} / 2 \mathrm{HCl}\) solution. The resulting liquid required \(25 \mathrm{~mL}\) of \(\mathrm{N} / \mathrm{S} \mathrm{NaOH}\) solution to neutralise it completely. Calculate the equivalent mass of the metal carbonate.

\(0.6 \mathrm{~g}\) of an organic compound was analysed: The ammonia thus produced was absorbed in \(90 \mathrm{~mL} \mathrm{~N} / 9 \mathrm{H}_{2} \mathrm{SO}_{4}\). The remaining acid required \(20 \mathrm{~mL} 0.1 \mathrm{NNaOH}\) for neutralisation. Calculate the percentage of nitrogen in the compound.

\(50 \mathrm{~mL}\) of \(0.2 \mathrm{~N} \mathrm{KMnO}_{4}\) is required for complete oxidation of \(0.45 \mathrm{~g}\) of anhydrous oxalic acid. Calculate the normality of oxalic acid solution.

To a solution of excess of KI in dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}, 25 \mathrm{~mL}\) of an unknown solution of \(\mathrm{KMnO}_{4}\) were added. The liberated iodine was exactly reduced by \(42.5 \mathrm{~mL}\) of \(\mathrm{N} / 10 \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) solution. Calculate the concentration of \(\mathrm{KMnO}_{4}\) solution.

\(1.64 \mathrm{~g}\) of a mixture of calcium carbonate and magnesium carbonate were dissolved in \(50 \mathrm{~mL}\) of \(0.8 \mathrm{~N}\) hydrochloric acid. The excess of the acid required \(16 \mathrm{~mL} \mathrm{~N} / 4\) sodium hydroxide solution for neutralisation. Find out the percentage composition of the mixture of two carbonates.

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