Question

Barium sulfate, \(\mathrm{BaSO}_{4}\), is made by the following reaction. \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{BaSO}_{4}(s)+2 \mathrm{NaNO}_{3}(a q)\) An experiment was begun with \(75.00 \mathrm{~g}\) of \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) and an excess of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\). After collecting and drying the product, \(64.45 \mathrm{~g}\) of \(\mathrm{BaSO}_{4}\) was obtained. Calculate the theoretical yield and percentage yield of \(\mathrm{BaSO}_{4}\)

Short answer

The theoretical yield of BaSO4 is calculated by using stoichiometry and molar masses, and the percentage yield is the actual yield divided by the theoretical yield, multiplied by 100%.

Step-by-step solution

Calculate the Molar Mass of Ba(NO3)2

Determine the molar mass (molecular weight) of Ba(NO3)2 by adding up the atomic masses of all the atoms. The molar mass of Ba(NO3)2 is calculated as follows: Ba (137.33 g/mol) + 2xN (2x14.01 g/mol) + 6xO (6x16.00 g/mol). Add these values together to find the molar mass.

Calculate Moles of Ba(NO3)2

Using the molar mass from Step 1, convert the given mass of Ba(NO3)2 into moles by using the formula: moles = mass (g) / molar mass (g/mol).

Determine the Stoichiometry

According to the balanced chemical equation, the molar ratio between Ba(NO3)2 and BaSO4 is 1:1. This means that 1 mole of Ba(NO3)2 will produce 1 mole of BaSO4.

Calculate Moles of BaSO4 Produced Theoretically

Using the moles of Ba(NO3)2 calculated in Step 2, find the theoretical yield in moles of BaSO4 since the stoichiometry is 1:1. The theoretical moles of BaSO4 is equal to the moles of Ba(NO3)2.

Calculate the Molar Mass of BaSO4

Determine the molar mass of BaSO4 by adding the atomic masses of Ba, S, and 4xO. The molar mass of BaSO4 is: Ba (137.33 g/mol) + S (32.07 g/mol) + 4xO (4x16.00 g/mol). Add these values together to get the molar mass of BaSO4.

Calculate the Theoretical Yield in Grams

Convert the theoretical moles of BaSO4 to grams by multiplying the moles by the molar mass of BaSO4 from Step 5. The theoretical yield in grams is the product of the moles of BaSO4 and its molar mass.

Calculate Percent Yield

Use the actual yield (64.45 g) and the theoretical yield calculated in Step 6 to determine the percentage yield. Percentage yield is calculated as follows: (actual yield / theoretical yield) x 100%.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that relates the quantities of reactants and products in chemical reactions. It involves the use of balanced chemical equations to calculate the amounts of substances consumed and produced. The equation provides the reactant-product relationships called stoichiometric factors, which indicate the proportional relationship between the reactants that react and the products that form.

For instance, in the reaction between barium nitrate and sodium sulfate to form barium sulfate and sodium nitrate, stoichiometry dictates that one mole of barium nitrate reacts with one mole of sodium sulfate to yield one mole of barium sulfate and two moles of sodium nitrate. The stoichiometric coefficients from the balanced equation are critical for these calculations. Understanding how to apply stoichiometry is fundamental when determining theoretical yields, a concept we will explore further in the subsequent section.

Theoretical Yield Calculation

Theoretical yield calculation is a prediction of the maximum amount of a product that can be produced in a chemical reaction based on the quantity of limiting reactant. It assumes that the reaction goes to completion and that there are no losses due to side reactions or other inefficiencies.

The step-by-step process to calculate the theoretical yield begins with finding the molar mass of the reactants and products. Using the balanced chemical equation, you then determine how many moles of each reactant you have and identify the limiting reactant—the one that will be completely used up first. From there, you can apply the stoichiometric ratios to find the moles of the product formed. Finally, you convert the moles of product back to grams using its molar mass. This final figure represents the theoretical yield, which is the maximum amount of product expected, an essential figure for calculating percentage yield.

Molar Mass

Molar mass is a key concept frequently used in stoichiometry. It is defined as the mass of one mole of a substance and is expressed in grams per mole (g/mol). One mole of any substance contains Avogadro's number (\(6.022 \times 10^{23}\)) of entities, whether they are atoms, molecules, ions, or other particles.

To calculate the molar mass, you need to sum up the atomic masses of every atom present in a molecule. The atomic masses can be found on the periodic table and typically represent the average weight of all isotopes of an atom. For instance, the molar mass of barium sulfate (\text{BaSO}_4\text) involves adding the atomic masses of one barium atom, one sulfur atom, and four oxygen atoms. Knowledge of molar mass allows you to convert between mass in grams and amount in moles, a fundamental step in stoichiometric calculations and in determining theoretical and percentage yields.