Question

Lithopone white paint is made by heating a mixture of \(\mathrm{BaS}\) and \(\mathrm{ZnSO}_{4}\) according to the equation \(\mathrm{BaS}+\mathrm{ZnSO}_{4} \rightarrow \mathrm{BaSO}_{4}+\mathrm{ZnS}\) What is the weight ratio of products \(\mathrm{BaSO}_{4}\) and \(\mathrm{ZnS}\) in the paint?

Short answer

The weight ratio of \(\mathrm{BaSO}_{4}\) and \(\mathrm{ZnS}\) in the Lithopone white paint is approximately \(2.39:1\).

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the given reaction is given as: \(\mathrm{BaS}+\mathrm{ZnSO}_{4} \rightarrow \mathrm{BaSO}_{4}+\mathrm{ZnS}\)

Calculate the molar masses of the products

To find the weight ratio of the products, we need to determine their molar masses. The molar mass can be calculated using the periodic table and summing the atomic masses for each atom in the compound. For \(\mathrm{BaSO}_{4}\): - Barium (Ba): 137.33 g/mol - Sulfur (S): 32.07 g/mol - Oxygen (O): 16.00 g/mol Molar mass of \(\mathrm{BaSO}_{4}\): \(137.33 + 32.07 + (4\times16.00) = 233.43\, \mathrm{g/mol}\) For \(\mathrm{ZnS}\): - Zinc (Zn): 65.38 g/mol - Sulfur (S): 32.07 g/mol Molar mass of \(\mathrm{ZnS}\): \(65.38 + 32.07 = 97.45\, \mathrm{g/mol}\)

Determine the weight ratio of the products

From the balanced chemical equation, we can see that the stoichiometry of the reaction is 1:1, which means that one mole of \(\mathrm{BaSO}_{4}\) is formed simultaneously with one mole of \(\mathrm{ZnS}\). Therefore, the weight ratio of \(\mathrm{BaSO}_{4}\) to \(\mathrm{ZnS}\) can be found by dividing their molar masses: Weight ratio of \(\mathrm{BaSO}_{4}\) to \(\mathrm{ZnS}\): \(\dfrac{233.43}{97.45} =\dfrac{11672.12}{4872.25} = 2.39\) Therefore, the weight ratio of \(\mathrm{BaSO}_{4}\) and \(\mathrm{ZnS}\) in the white paint is approximately \(2.39:1\).

Key concepts

Balanced Chemical Equation

A balanced chemical equation is a representation of a chemical reaction where the numbers of atoms for each element are the same on both sides of the equation. This is crucial because it reflects the law of conservation of mass, meaning that matter cannot be created or destroyed in a chemical reaction.
In the example provided with lithopone white paint, we have the chemical equation:

• \[ \text{BaS} + \text{ZnSO}_{4} \rightarrow \text{BaSO}_{4} + \text{ZnS} \]

This equation is already balanced. Each side has one barium (Ba), one sulfur (S) combined differently in compounds, and one zinc (Zn), signifying conservation of matter.
Balanced equations are important because they allow us to predict and measure the exact amounts of reactants and products involved in a chemical reaction.

Molar Mass

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by the amount of substance in moles. It allows us to convert between the mass of a substance and the amount of substance.
The molar mass is calculated using the atomic masses of elements found on the periodic table. For example, in the given reaction:

• The molar mass of \(\text{BaSO}_{4}\) is calculated as: \[137.33 \text{ (Ba)} + 32.07 \text{ (S)} + (4 \times 16.00 \text{ (O)}) = 233.43 \, \text{g/mol}\]
• For \(\text{ZnS}\), it is: \[65.38 \text{ (Zn)} + 32.07 \text{ (S)} = 97.45 \, \text{g/mol}\]

Understanding molar mass helps in determining how much of each product is formed, given the starting quantities of reactants in a chemical reaction.

Weight Ratio

The weight ratio in chemistry refers to the comparative mass of one substance to another, derived from their molar masses. In the context of a chemical reaction, the weight ratio of products is useful when considering the formulation of a mixture or product like paint.
To find the weight ratio of the products \(\text{BaSO}_{4}\) and \(\text{ZnS}\) in the paint, we use their molar masses. The reaction shows a 1:1 mole ratio of \(\text{BaSO}_{4}\) and \(\text{ZnS}\), so the weight ratio is derived directly from:

• \[\text{Weight ratio} = \frac{\text{Molar mass of } \text{BaSO}_{4}}{\text{Molar mass of } \text{ZnS}} = \frac{233.43}{97.45} \approx 2.39\]

This means for every gram of \(\text{ZnS}\), we have approximately 2.39 grams of \(\text{BaSO}_{4}\), illustrating the dominance of \(\text{BaSO}_{4}\) by weight in the product mixture.

Chemical Reaction

A chemical reaction is the process where substances called reactants are transformed into products. This transformation involves breaking bonds in the reactants and forming new bonds to create the products. The characteristics of chemical reactions are captured in chemical equations.
In our reaction for producing lithopone paint:

• The reactants are \(\text{BaS}\) and \(\text{ZnSO}_{4}\).
• The products are \(\text{BaSO}_{4}\) and \(\text{ZnS}\).

This reaction is particularly important as it generates solid compounds that contribute to the pigmentation in paint.
Understanding chemical reactions is vital in chemistry as they form the basis for the creation of new materials, energy transformation, and biochemical processes. Each reaction is different, with some requiring energy input to proceed, while others release energy or occur spontaneously.