Problem 52 - Chemistry Matter and Change

Question

If 45.98 \(\mathrm{g}\) of sodium combines with an excess of chlorine gas to form 116.89 \(\mathrm{g}\) of sodium chloride, what mass of chlorine gas is used in the reaction?

Step-by-Step Solution

Answer

70.91 g of chlorine gas is used in the reaction.

Step 1: Understand the Problem

Read the problem statement carefully. We are given the mass of sodium (Na) and the mass of sodium chloride (NaCl) formed. We need to find the mass of chlorine gas (Cl2) that reacts with sodium.

Step 2: Write the Chemical Equation

The chemical reaction between sodium and chlorine gas to form sodium chloride is:\[ 2 \mathrm{Na} + \mathrm{Cl}_2 \rightarrow 2 \mathrm{NaCl} \] This equation tells us that 2 atoms of sodium react with 1 molecule of chlorine gas to form 2 formula units of sodium chloride.

Step 3: Apply the Law of Conservation of Mass

The law of conservation of mass states that the mass of the reactants equals the mass of the products. Therefore, we can say: \[ \text{Mass of Na} + \text{Mass of Cl}_2 = \text{Mass of NaCl} \] Substituting the known values: \[ 45.98 \mathrm{g} + \text{Mass of Cl}_2 = 116.89 \mathrm{g} \]

Step 4: Solve for the Unknown Mass

Rearrange the equation from Step 3 to find the mass of chlorine gas: \[ \text{Mass of Cl}_2 = 116.89 \mathrm{g} - 45.98 \mathrm{g} \] Calculate the result: \[ \text{Mass of Cl}_2 = 70.91 \mathrm{g} \]

Key Concepts

Chemical Equations

Chemical equations are a symbolic way to represent chemical reactions. They showcase how substances react together and what they form. In our example, sodium (Na) reacts with chlorine (\(\text{Cl}_2\)) to produce sodium chloride (NaCl). This is written as: \[2\text{Na} + \text{Cl}_2 \rightarrow 2\text{NaCl}\] In this equation:

• The reactants are the starting substances: sodium and chlorine gas.
• The product is what you end up with: sodium chloride.
• Coefficients (the numbers in front of the substances) show the ratio of molecules or atoms involved in the reaction. Here, 2 sodium atoms react with each chlorine molecule to form 2 formula units of sodium chloride.

Chemical equations must be balanced, meaning they obey the law of conservation of mass, which we'll explore next.Balancing chemical equations is crucial in predicting how much product we can get from given reactants.

Conservation of Mass

The law of conservation of mass is fundamental in chemistry. It states that mass cannot be created or destroyed in a chemical reaction. Instead, the mass of the reactants must equal the mass of the products. This means that, in terms of weight, whatever you start with, you must also end with. Let's apply this law to our exercise: - You start with 45.98 g of sodium. - You produce 116.89 g of sodium chloride. - The difference, 70.91 g, accounts for the chlorine that reacted. Therefore, the mass of reactants (sodium and chlorine gas) equals the mass of the product (sodium chloride). This keeps the universe neat and balanced. If you understand this, you can solve many problems in chemistry by ensuring that the total mass on both sides of an equation matches.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with quantitatively measuring and calculating the reactants and products in chemical reactions. Imagine you have a recipe for a specific chemical substance—stoichiometry tells you how much of each ingredient you need. Using the balanced chemical equation, we know that: - 2 moles of sodium react with 1 mole of chlorine gas to yield 2 moles of sodium chloride. To find out the mass of chlorine gas used, you use stoichiometry and the following steps: 1. Calculate the total mass of sodium chloride formed. 2. Subtract the mass of sodium used. 3. The result is the mass of chlorine gas used. Thus, stoichiometry allows you to relate masses and numbers of moles in a chemical reaction, ensuring precise calculations and efficient reactions. It is an essential skill for any chemist or science student to have.