Problem 59 - General Chemistry: Principles and Modern Applications

Question

How many grams of sodium must react with \(155 \mathrm{mL}\) \(\mathrm{H}_{2} \mathrm{O}\) to produce a solution that is \(0.175 \mathrm{M} \mathrm{NaOH} ?\) (Assume a final solution volume of \(155 \mathrm{mL}\) ) $$ 2 \mathrm{Na}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$

Step-by-Step Solution

Answer

Around 0.624 grams of Sodium is required to produce a 0.175 M NaOH solution in 155 mL.

Step 1: Calculate moles of NaOH

In order to determine the amount of Sodium, the amount of moles of sodium hydroxide in the solution should firstly be calculated. The molarity of a solution is calculated by the number of moles of solute per liter of solution (M = moles/L). In this case, M = 0.175M and V = 155 mL = 0.155 L. Apply the formula \(Molarity = \frac{moles}{volume}\) to calculate moles. So, \(moles = Molarity \times Volume = 0.175 M \times 0.155 L = 0.0271 moles\) of NaOH.

Step 2: Apply the stoichiometry from chemical equation

According to the balanced chemical equation, 2 moles of Na produce 2 moles of NaOH. Therefore, the moles of Na needed to produce 0.0271 moles of NaOH is also 0.0271 moles.

Step 3: Calculate mass of Sodium

We know the molar mass of Hydrogen (Na) is about 23 g/mol. Therefore, the amount of Sodium needed is \(mass = moles \times molar mass = 0.0271 mol \times 23 g/mol = 0.624 g\).

Key Concepts

Molarity

Molarity is a crucial concept when dealing with solutions in chemistry. It represents the concentration of a solute in a solution. Understanding molarity is important for calculating the amount of substance dissolved in a specific volume of liquid.

To calculate molarity, use the formula \( \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). This form of concentration allows for the calculation of how substances interact in reactions. If you know the molarity along with the volume of your solution, you can determine the moles of solute present.

For instance, in our problem, with a molarity of 0.175 M and a solution volume of 0.155 L, you can calculate the moles of NaOH by multiplying them together, which results in 0.0271 moles of NaOH. This is a fundamental step in calculating how much of the initial substance, like sodium, is needed in a chemical reaction.

Sodium Reaction

Understanding sodium reactions, particularly with water, is key to grasping the stoichiometric calculations involved in the exercise. Sodium, a reactive metal, reacts with water to form sodium hydroxide (NaOH) and hydrogen gas (H2). This particular reaction is highly exothermic, meaning it releases a significant amount of energy in the form of heat.

The balanced chemical equation for the reaction is:

• 2 Na(s) + 2 H2O(l) → 2 NaOH(aq) + H2(g)

In this equation, two moles of sodium react with two moles of water to produce two moles of sodium hydroxide and hydrogen gas. This indicates a one-to-one molar ratio between sodium and sodium hydroxide. Therefore, for any given amount of NaOH produced, the same number of moles of sodium is required.

In our scenario, since 0.0271 moles of NaOH are produced, you'll need an equivalent 0.0271 moles of sodium to complete the reaction.

Chemical Equations

Chemical equations represent the reactants and products in a chemical reaction. They reflect the conservation of mass and the relationship between reactants and products.

The equation needs to be balanced, showcasing an equal number of atoms for each element on both sides. This is fundamental for determining the stoichiometry, or the quantitative part of chemistry that deals with the proportional relationships between substances.

In our example, the balanced equation is:

• 2 Na(s) + 2 H2O(l) → 2 NaOH(aq) + H2(g)

This tells us that the reaction occurs at a one-to-one molar ratio between sodium and sodium hydroxide. You can use this stoichiometric relationship to calculate how much of each substance you need or will produce.

In practice, knowing the balanced equation allows you to derive the amount of reactants needed to get a desired amount of product. Specifically, with the stoichiometry of 2:2:2 entries, you can predict that the NaOH produced is directly equivalent to the amount of Na used. These calculations ensure efficient and proper use of chemicals in reactions.