The percentage yield of nitric acid is 95\(\% .\) If 9.88 \(\mathrm{kg}\) of nitrogen dioxide react, what mass of nitric acid is isolated? $$3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$$

When performing chemical reactions, the percentage yield is a measure of the efficiency of a reaction. It is calculated by taking the actual yield (the amount of product obtained) and dividing it by the theoretical yield (the amount of product that could be formed based on stoichiometry), then multiplying the result by 100 to get a percentage.

For example, if the theoretical yield of a reaction is 10 grams but only 9 grams of product were actually isolated, the percentage yield would be \( \frac{9 g}{10 g} \times 100\% = 90\% \).

The percentage yield can be influenced by factors such as incomplete reactions, impurities, or losses during product recovery. Thus, it's rare to achieve a 100% yield in reality. Knowing the percentage yield helps in evaluating the reaction's practicality and cost-efficiency.

The molar mass of a compound is the mass of one mole of its molecules and is measured in grams per mole (g/mol). To determine the molar mass, we add together the atomic masses of each element within the compound according to its chemical formula.

For instance, to find the molar mass of nitric acid \( \mathrm{HNO}_3 \), we sum the masses of hydrogen \(1.01 \, g/mol\), nitrogen \(14.01 \, g/mol\), and oxygen \(16.00 \, g/mol\, multiplied by 3 since there are three oxygen atoms\), resulting in a molar mass of \(63.02\, g/mol\).

Being able to determine molar mass is fundamental in stoichiometry as it allows for conversion between mass and moles, crucial for quantitatively analyzing chemical reactions.

Chemical stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It helps predict how much product will form from a given amount of reactant or how much reactant is needed to make a desired amount of product.

Stoichiometry is grounded on the law of conservation of mass and the balanced chemical equation. For example, in the reaction \(3 \mathrm{NO}_2(g) + \mathrm{H}_2\mathrm{O}(g) \rightarrow 2\mathrm{HNO}_3(aq) + \mathrm{NO}(g)\), the ratio of moles of nitrogen dioxide to moles of nitric acid is 3:2. This ratio means that every three moles of \(\mathrm{NO}_2\) should theoretically yield two moles of \(\mathrm{HNO}_3\).

By using these ratios, we can perform calculations to scale up or down the amounts needed for a reaction or to predict the yield from a given quantity of starting material.

The theoretical yield is the maximum amount of product that could be produced in a chemical reaction if everything reacted completely. It's calculated based on the reaction's balanced equation and the limiting reactant, which is the reactant that will run out first, limiting the amount of product formed.

To calculate the theoretical yield, one must first identify the mole ratio of the reactant to the product from the balanced equation. Then, determine the amount of moles of the reactant being used. Multiply the moles of the reactant by the mole ratio to find the moles of product that should form theoretically. Finally, convert this to mass using the molar mass of the product.

In practice, the actual yield will often be less than the theoretical yield due to various factors such as side reactions, incomplete reactions, or loss of product during purification.