Question

The principal anion and cation in Lake Huron, one of the Great Lakes in North America, are respectively hydrogen carbonate and calcium. The concentration of the former is approximately \(1.05 \mathrm{mmol} \mathrm{L}^{-1}\). Calculate the mass of solid calcium carbonate that would remain if \(250 \mathrm{~mL}\) of Lake Huron water is evaporated to dryness.

Short answer

0.02625 g of calcium carbonate would remain.

Step-by-step solution

Determine moles of hydrogen carbonate

First, let's calculate the moles of hydrogen carbonate (HCO₃⁻) in 250 mL of lake water. The concentration of HCO₃⁻ is given as 1.05 mmol/L. Convert this to moles first: \[ \text{moles of } \text{HCO}_3^- = 1.05 \times 10^{-3} \text{ mol/L} \times 0.250 \text{ L} = 2.625 \times 10^{-4} \text{ mol}. \] This is the total amount of HCO₃⁻ present in the volume of water.

Moles of calcium carbonate formed

In the reaction where calcium ions \((\text{Ca}^{2+})\) combine with hydrogen carbonate ions \((\text{HCO}_3^-)\) to form calcium carbonate \((\text{CaCO}_3)\) and water, the ratio is 1:1, based on the balanced chemical equation: \[ \text{Ca}^{2+} + \text{HCO}_3^- \rightarrow \text{CaCO}_3 + \text{H}_2\text{O}. \] Therefore, the moles of \(\text{CaCO}_3\) formed is also \(2.625 \times 10^{-4} \text{ mol}.\)

Calculate the mass of calcium carbonate

Using the moles calculated, we find the mass of calcium carbonate. The molar mass of calcium carbonate (\(\text{CaCO}_3\)) is 100.09 g/mol. So, the mass is calculated as follows: \[ \text{mass of } \text{CaCO}_3 = 2.625 \times 10^{-4} \text{ mol} \times 100.09 \text{ g/mol} = 0.02625 \text{ g}. \] This is the mass of solid calcium carbonate that would remain after evaporation.

Key concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the calculation of reactants and products in chemical reactions. It provides a way to understand how substances interact and transform based on a balanced chemical equation. In the context of the Lake Huron exercise, stoichiometry helps us determine the amount of calcium carbonate (\( \text{CaCO}_3 \)) that can be formed when hydrogen carbonate (\( \text{HCO}_3^- \)) reacts with calcium ions (\( \text{Ca}^{2+} \)).

To use stoichiometry effectively:

• Start with a balanced chemical equation to ensure conservation of mass and charge.
• Identify the mole ratio between reactants and products from the equation.
• Use the concentrations and volumes provided to calculate moles of reactants.
• Determine the moles of products formed using the mole ratio.

In this exercise, a 1:1 ratio exists between hydrogen carbonate ions and calcium carbonate in the reaction (\( \text{Ca}^{2+} + \text{HCO}_3^- \rightarrow \text{CaCO}_3 + \text{H}_2\text{O} \)). This means that for every mole of hydrogen carbonate, one mole of calcium carbonate is produced. This direct relationship simplifies the calculation of product formation.

Lake Water Chemistry

Lake water chemistry involves studying the composition of ions and molecules dissolved in water bodies like lakes, which play crucial roles in aquatic ecosystems. Key ions in Lake Huron, such as hydrogen carbonate (\( \text{HCO}_3^- \)) and calcium (\( \text{Ca}^{2+} \)), are vital to maintaining the chemical balance in the lake.

Here are some essential points about lake water chemistry:

• Lake chemistry is influenced by both natural processes and human activities, which can alter ionic concentrations.
• Hydrogen carbonate acts as a buffer, maintaining the pH of the lake by reacting with acids and bases.
• Calcium ions contribute to the hardness of water, affecting both ecological and industrial activities.

The interaction between these ions is vital for processes like the precipitation of calcium carbonate, which can affect lake sediment formation. Understanding this chemistry helps in managing water quality and mitigating environmental impacts.

Calcium Carbonate Precipitation

Calcium carbonate precipitation is a chemical process where calcium ions and carbonate ions form solid calcium carbonate (\( \text{CaCO}_3 \)). This process can occur naturally in lakes, contributing to sediment buildup, and is important for various environmental and industrial applications.

Key aspects of calcium carbonate precipitation include:

• It often occurs when the water is saturated with \( \text{Ca}^{2+} \) and \( \text{HCO}_3^- \), leading them to bond and form a solid.
• Changes in temperature, pH, and ionic strength can influence the rate and extent of precipitation.
• This process is important for forming geological structures like limestone and provides a habitat for aquatic life.

In the given exercise, when Lake Huron's water evaporates, the concentration of these ions increases, promoting precipitation. This results in the formation of calcium carbonate deposits, which remain as a solid residue post evaporation.