Problem 145 - Chemistry The Molecular Science

Question

A 4.22-g mixture of calcium chloride and sodium chloride was treated so that all of the calcium was converted to calcium carbonate. This product was then heated, converting it to \(0.959 \mathrm{~g}\) pure calcium oxide. Calculate the mass percent of calcium chloride in the original mixture.

Step-by-Step Solution

Answer

The mass percent of calcium chloride in the mixture is approximately 45.02%.

Step 1: Determine the Moles of Calcium Oxide

First, calculate the moles of calcium oxide (\(\text{CaO}\)) using its given mass, 0.959 g. The molar mass of \(\text{CaO}\) is 56.08 g/mol. Thus:\[moles\ of\ CaO = \frac{0.959\ g}{56.08\ g/mol}\approx 0.0171\ mol\]

Step 2: Relate Moles of Calcium Oxide to Calcium Chloride

Since \(\text{CaO}\) is derived from calcium, it corresponds to the calcium from calcium chloride (\(\text{CaCl}_2\)) in the original mixture. The number of moles of calcium in \(\text{CaO}\) equals the number of moles of calcium in \(\text{CaCl}_2\).

Step 3: Calculate the Mass of Calcium Chloride

Now that we know moles of calcium (0.0171 mol) are moles of \(\text{CaCl}_2\), we use the molar mass of \(\text{CaCl}_2\) (110.98 g/mol) to find the mass:\[\text{mass\ of\ CaCl}_2 = 0.0171\ mol \times 110.98\ g/mol \approx 1.9\ g\]

Step 4: Calculate Mass Percent of Calcium Chloride

To find the mass percent of \(\text{CaCl}_2\) in the mixture, divide the mass of \(\text{CaCl}_2\) by the total mass of the mixture and multiply by 100:\[\text{Mass\ Percent\ of\ CaCl}_2 = \left(\frac{1.9\ g}{4.22\ g}\right) \times 100\approx 45.02\%\]

Step 5: Verify and Interpret the Result

Ensure the logic and calculations align with the question context. The steps confirm the outcome as correct.

Key Concepts

Mass Percent

Mass percent is a way to express the concentration of one component in a mixture or solution. It helps to understand how much of a specific component is present in a given mass of the entire mixture. To calculate mass percent, you use the formula:

• Mass percent = (mass of the component / total mass of the mixture) × 100

This concept is particularly useful in chemistry when determining the composition of compounds and mixtures. For example, in the original problem, we calculated the mass percent of calcium chloride in a 4.22 g mixture by finding how much of that weight was calcium chloride after certain chemical conversions. This provides a clearer understanding of its proportion within the total mixture.

Calcium Chloride

Calcium chloride (

• chemical formula: CaCl₂

) is a versatile compound that has many uses, ranging from road de-icing to acting as a firming agent in food. It's composed of calcium ions (Ca²⁺) and chloride ions (Cl^-). In the context of our exercise, calcium chloride reacts in a series of chemical transformations:

• In the first step, calcium in the \( ext{CaCl}_2\) is converted into calcium carbonate (\( ext{CaCO}_3\)).
• Then, when heated, \( ext{CaCO}_3\) turns into calcium oxide (\( ext{CaO}\)) and releases carbon dioxide (\( ext{CO}_2\)).

Understanding these transformations helps in evaluating how much calcium (and thus calcium chloride) was present initially in the sample.

Chemical Conversion

Chemical conversion is when a substance changes into a different chemical substance through a chemical reaction. Such conversions are essential in determining the composition of compounds when direct analysis isn't feasible.

1. In our exercise, the calcium in calcium chloride underwent multiple conversions;
2. First, it turned into calcium carbonate;
3. Latterly, calcium carbonate was further heated and converted into calcium oxide.

Calculating the moles of the new substance formed provides a back-route to understand the original amount of the starting material.
By using these conversions along with stoichiometry, we can deduce quantities like the mass percent of a component in complex mixtures. This is usually achieved by leveraging the known molar masses of the substances involved.
Such conversions not only help in academic exercises but are crucial in industry where raw materials often undergo transformations before becoming a finished product.