Question

How many grams of baking soda, \(\mathrm{NaHCO}_{3}\), are needed to react with \(162 \mathrm{~mL}\) of stomach acid having an \(\mathrm{HCl}\) concentration of \(0.052 \mathrm{M}\) ?

Short answer

8.43 grams of \(\mathrm{NaHCO}_{3}\) are needed.

Step-by-step solution

Write the chemical equation

Firstly, write down the balanced chemical equation of baking soda reacting with hydrochloric acid. The reaction is \(\mathrm{NaHCO}_{3} + \mathrm{HCl} \rightarrow \mathrm{NaCl} + \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\).

Calculate the moles of HCl

Next, calculate the moles of HCl using the volume and molarity: \(\text{moles of HCl} = \text{volume in liters} \times \text{molarity}\). Convert the volume from milliliters to liters by dividing by 1000. Here, \(\text{moles of HCl} = 0.162 \mathrm{L} \times 0.052 \mathrm{M}\).

Establish mole ratio

Using the balanced chemical equation, establish the mole ratio between \(\mathrm{NaHCO}_{3}\) and \(\mathrm{HCl}\). The ratio is 1:1.

Calculate moles of NaHCO3

The moles of \(\mathrm{NaHCO}_{3}\) will be equal to the moles of \(\mathrm{HCl}\) since the mole ratio is 1:1. So, the moles of \(\mathrm{NaHCO}_{3}\) needed is the same value calculated in Step 2.

Calculate the mass of NaHCO3

Finally, calculate the mass of \(\mathrm{NaHCO}_{3}\) needed by using its molar mass (84.01 g/mol). \(\text{Mass of NaHCO}_{3} = \text{moles of NaHCO}_{3} \times \text{molar mass} = (0.162 \times 0.052) \mathrm{mol} \times 84.01 \mathrm{g/mol}\).

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantities of substances consumed and produced in chemical reactions. It is a fundamental concept for ensuring that reactions are accurately described and controlled. To understand stoichiometry, imagine you are baking a cake, and the recipe calls for specific amounts of flour, sugar, and eggs. Just like in cooking, stoichiometry requires precise measurement of reactants to produce the desired amount of product.

To solve stoichiometry problems, start by writing a balanced chemical equation. This represents the recipe for the chemical reaction, showing how reactants are transformed into products. Then, use the coefficients of the balanced equation to establish a mole ratio, which acts like the ratio of ingredients in your recipe. Lastly, perform calculations to find out how much reactant is needed or how much product is formed. This process allows us to predict and measure the outcomes of chemical reactions in a quantitative manner.

Chemical Reactions

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. Every reaction is governed by the conservation of mass, indicating that the total mass of the reactants equals the total mass of the products. In the case of baking soda reacting with hydrochloric acid, the reaction produces sodium chloride, carbon dioxide, and water.

This transformation can be depicted in a chemical equation, which must be balanced to reflect the conservation of atoms. Balancing involves ensuring that the number of atoms for each element is the same on both sides of the equation. Understanding the types of reactions (synthesis, decomposition, single replacement, double replacement, combustion) helps in predicting the products of a reaction and provides a solid foundation for mastering stoichiometry.

Molarity

Molarity is an expression of the concentration of a solution, defined as moles of solute per liter of solution. It is represented by the symbol 'M' and is a crucial tool for communicating the strength of a solution in chemistry. When working with chemical solutions, knowing the molarity allows us to relate volumes of liquid solutions to the number of moles of a solute.

To calculate molarity, divide the number of moles of solute by the volume of the solution in liters. In the exercise, the molarity of hydrochloric acid (\( HCl \) allows us to determine how many moles of acid are present in a given volume of stomach acid. This value is paramount to continuing with stoichiometry calculations in order to find the mass of baking soda needed for the reaction.

Mole Concept

The mole concept is to chemistry what the dozen is to shopping; it is a count of entities. One mole represents approximately \( 6.022 \times 10^{23} \) entities, whether they are atoms, molecules, ions, or other particles. The importance of the mole lies in its ability to link the microscopic world of atoms with the macroscopic world we can measure. By using the mole concept, we can translate the number of particles involved in a chemical reaction to a mass that we can weigh out in the lab.

In the exercise, we use the mole concept to convert the number of moles of baking soda to grams. The molar mass of \( \mathrm{NaHCO}_3 \) (the mass of one mole of \( \mathrm{NaHCO}_3 \)) is an essential factor for this conversion. This way, chemists can accurately determine how much of a substance is required for a reaction, just like measuring ingredients for our cake recipe earlier.