Question

Baking powder consists of a mixture of cream of tartar (potassium hydrogen tartrate, \(\mathrm{KHC}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\), molecular weight \(=188 \mathrm{~g} /\) mole \()\) and baking soda (sodium bicarbonate, \(\mathrm{NaHC} 0_{3}\), molecular weight \(=84 \mathrm{~g} /\) mole \()\). These two components react according to the equation \(\mathrm{KHC}_{4} \mathrm{H}_{4} \mathrm{O}_{6}+\mathrm{NaHCO}_{3} \rightarrow \mathrm{KNaC}_{4} \mathrm{H}_{4} \mathrm{O}_{6}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) How much baking soda must be added to \(8.0 \mathrm{~g}\) of cream of tartar for both materials to react completely?

Short answer

To find the amount of baking soda needed to react completely with 8.0g of cream of tartar, we first calculate the moles of cream of tartar: \[\text{moles of cream of tartar} = \frac{8.0 g}{188 g/mol} = 0.0426 \text{ moles}\] Since the molar ratio between cream of tartar and baking soda in the given reaction is 1:1, the moles of baking soda needed is equal to the moles of cream of tartar. Then, we calculate the mass of baking soda required: \[\text{mass of baking soda} = \text{moles of baking soda} \times 84 g/mol = 0.0426 \text{ moles} \times 84 g/mol = 3.58 g\] Hence, 3.58g of baking soda must be added to 8.0g of cream of tartar for both materials to react completely.

Step-by-step solution

Calculate the number of moles of cream of tartar

To determine how much baking soda is needed, we first need to find out how many moles of cream of tartar the 8.0g consists of. We can do this using its molecular weight, which is given as 188 g/mol. The formula for calculating moles is: \[moles = \frac{mass}{molecular~weight}\] Using the given information, \[moles = \frac{8.0~g}{188~g/mol}\]

Determine the molar ratio between the reactants

Next, we need to determine the molar ratio between cream of tartar and baking soda in the given chemical equation: \[\mathrm{KHC}_{4} \mathrm{H}_{4} \mathrm{O}_{6} + \mathrm{NaHCO}_{3} \rightarrow \mathrm{KNaC}_{4} \mathrm{H}_{4} \mathrm{O}_{6} + \mathrm{H}_{2} \mathrm{O} + \mathrm{CO}_{2}\] The equation shows that 1 mole of cream of tartar reacts with 1 mole of baking soda.

Calculate the number of moles of baking soda required

Now that we have the moles of cream of tartar and the molar ratio between the reactants, we can calculate the number of moles of baking soda required for the reaction. Since the ratio is 1:1, the moles of baking soda needed is equal to the moles of cream of tartar. moles of baking soda = moles of cream of tartar

Calculate the mass of baking soda required

Finally, we will calculate the mass of baking soda required for the reaction using its molecular weight of 84 g/mol: \[mass = moles \times molecular~weight\] Using the moles of baking soda we found above and the molecular weight, mass of baking soda = moles of baking soda × 84 g/mol Once you calculate the mass of baking soda, you will have the amount needed to react completely with 8.0g of cream of tartar.

Key concepts

Mole Concept

Understanding the mole concept is essential when dealing with chemical quantities in reactions. A mole is a unit used to express the amount of a chemical substance, similar to using 'dozen' for eggs. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10^23 particles – atoms, ions, or molecules, depending on the substance.

In stoichiometry problems, like the one involving baking powder, the mole concept allows us to convert between the mass of a substance and the number of moles using the formula:
\[moles = \frac{mass}{molecular~weight}\].
For instance, in the given exercise, calculating the number of moles of cream of tartar from its mass and molecular weight is a straightforward application of the mole concept.

Chemical Reaction

A chemical reaction is a process where reactants transform into products. Understanding the balanced chemical equation, as shown in the exercise with cream of tartar and baking soda, is crucial. It indicates the exact proportions in which substances react and form products. In this case, the equation tells us that one mole of potassium hydrogen tartrate reacts with one mole of sodium bicarbonate to produce potassium sodium tartrate, water, and carbon dioxide.

This balance is pivotal in stoichiometry, as it governs the quantities needed for a reaction to proceed completely without leaving any excess reactants.

Reactant Molar Ratio

The reactant molar ratio from a balanced chemical equation indicates the proportions of reactants that will react with each other. This ratio is derived by looking at the coefficients in front of each reactant in the equation. In the exercise problem, the reaction between cream of tartar and baking soda has a molar ratio of 1:1, indicating that they react on a one-to-one basis.

Whenever you are given the quantity of one reactant, like the 8.0g of cream of tartar in our example, you can use the molar ratio to find the needed quantity of the other reactant, ensuring a complete reaction with no leftover reactants.

Molecular Weight

Molecular weight, also known as molecular mass, is the sum of the atomic weights of all the atoms in a molecule. It is expressed in atomic mass units (amu) or grams per mole (g/mol). In stoichiometry, knowing the molecular weight of substances allows you to convert between mass and moles of a substance, as demonstrated in the step-by-step baking powder problem.

For example, the molecular weight of cream of tartar (KHC₄H₄O₆) is given as 188 g/mol, which is crucial information needed to determine how much of it is present in moles when given in grams. This conversion is the first step in solving many stoichiometry problems, including the example exercise.