Question

Sodium metal reacts violently with water to form NaOH and release hydrogen gas. Suppose that 10.0 g of Na react completely with 1.00 L of water and the final solution volume is 1.00 L. a. What is the molar mass of NaOH? b. Write a balanced equation for the reaction. c. What is the molarity of the NaOH solution formed by the reaction?

Short answer

a. The molar mass of NaOH is 40.00 g/mol. b. The balanced equation is \[2Na + 2H_2O \rightarrow 2NaOH + H_2\]. c. The molarity of the NaOH solution is 0.435 M.

Step-by-step solution

- Calculate the Molar Mass of NaOH

To find the molar mass of NaOH, sum up the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):\texpected_mass_of_Na = 22.99 \text{ g/mol}\texpected_mass_of_O = 16.00 \text{ g/mol}\texpected_mass_of_H = 1.01 \text{ g/mol}Thus, the molar mass of NaOH is:\t\[22.99 + 16.00 + 1.01 = 40.00 \text{ g/mol}\]

- Write a Balanced Equation for the Reaction

Sodium reacts with water according to the following balanced chemical equation: \t\[2Na + 2H_2O \rightarrow 2NaOH + H_2\]

- Calculate the Moles of Sodium (Na)

Find the moles of sodium involved in the reaction by using its molar mass:\t\[ \text{number_of_moles_Na} = \frac{ \text{mass_Na} }{ \text{molar_mass_Na} } = \frac{10.0 \text{ g}}{22.99 \text{ g/mol}} = 0.435 \text{ mol} \tag{1}\]

- Calculate the Moles of NaOH Formed

Based on the balanced equation, 2 moles of Na produce 2 moles of NaOH, so:\t\[ \text{moles_NaOH} = \text{moles_Na} = 0.435 \text{ mol}\]

- Calculate the Molarity of the NaOH Solution

Molarity is calculated using the formula:\t \[ M = \frac{ \text{moles_NaOH} }{ \text{volume_solution} } = \frac{0.435 \text{ mol}}{1.00 \text{ L}} = 0.435 \text{ M}\]Therefore, the molarity of the NaOH solution is 0.435 M.

Key concepts

molar mass

Molar mass is a fundamental concept in chemistry. It represents the mass of one mole of a given substance. To calculate the molar mass, you need to sum the atomic masses of all atoms in a molecule. For example, in NaOH (sodium hydroxide), we find the molar mass by summing the atomic masses of sodium (Na), oxygen (O), and hydrogen (H):

• Mass of Na: 22.99 g/mol
• Mass of O: 16.00 g/mol
• Mass of H: 1.01 g/mol

Adding these together, the molar mass of NaOH becomes 40.00 g/mol: \[ 22.99 + 16.00 + 1.01 = 40.00 \text{g/mol} \] Understanding molar mass is essential for converting between grams and moles, which is a foundational skill in chemistry.

balanced chemical equation

A balanced chemical equation accurately represents a chemical reaction showing the same number of each type of atom on both sides of the equation. This balance adheres to the law of conservation of mass, which states mass cannot be created or destroyed in a chemical reaction. Let's take the example of sodium reacting with water:

• Unbalanced: Na + H₂O → NaOH + H₂

This equation isn't balanced because the number of Na, O, and H atoms differ on each side. Balancing involves adjusting coefficients to ensure equal numbers of each atom on both sides:

• Balanced: 2Na + 2H₂O → 2NaOH + H₂

This tells us 2 moles of sodium react with 2 moles of water to produce 2 moles of NaOH and 1 mole of hydrogen gas.

molarity calculation

Molarity is a measure of the concentration of a solution, denoted as mol/L or M. It is calculated using the formula:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] For example, if you dissolve 0.435 moles of NaOH in 1 liter of water, the molarity is:
\[ M = \frac{0.435 \text{ moles}}{1.00 \text{ L}} = 0.435 \text{ M} \] Accurate molarity calculations are crucial in laboratory settings for preparing solutions with the desired concentrations. They are fundamental in various applications, including titrations and reactions requiring precise stoichiometry.

chemical reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. In the reaction between sodium and water, sodium hydroxide and hydrogen gas are formed:
\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \] Here,

• Sodium (Na) reacts as a metal with water (H₂O).
The product is sodium hydroxide (NaOH), a strong base, and hydrogen gas (H₂), which is released.

Such reactions are exothermic, releasing heat. Understanding chemical reactions is fundamental in predicting product formation, energy changes, and reaction rates, all crucial for fields like chemistry, biology, and engineering.

stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the balanced equation to determine the ratio of molecules or moles of each substance involved. Let's refer to our reaction:
\[ 2Na + 2H_2O \rightarrow 2NaOH + H_2 \] From this, we see:

• 2 moles of Na produce 2 moles of NaOH
• 2 moles of H₂O produce 1 mole of H₂

To find how many moles of NaOH can be obtained from a certain amount of Na, use the ratio from the balanced equation. For instance, if reacting 10.0 g of Na (which is 0.435 moles):

• Moles of NaOH = moles of Na = 0.435 moles

Mastering stoichiometry allows for precise predictions of product yields and necessary reactants, critical for efficient chemical manufacturing and laboratory work.