Question

Sodium metal reacts with water in the following singledisplacement reaction: $$ 2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(t) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) $$ Determine the limiting reactant and mass of \(\mathrm{H}_{2}\) gas produced when \(2.0 \mathrm{~g}\) of \(\mathrm{Na}\) is added to \(10.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\).

Short answer

The limiting reactant is Sodium (Na), and the mass of Hydrogen gas (H2) produced is approximately 0.088 g.

Step-by-step solution

Calculation of Moles for each Reactant

First, by using the molar mass of each substance (Na and H2O), calculate the number of moles for Sodium and water respectively. The molar mass of Na is roughly 22.99 g/mol, and for H2O is roughly 18.015 g/mol. \n\n For Sodium (Na): \n \( \frac{2.0 \, g}{22.99 \, g/mol} = 0.087 \, moles\) \n For Water (H2O): \n \( \frac{10.0 \, g}{18.015 \, g/mol} = 0.555 \, moles\)

Determining the Limiting Reactant

The stoichiometric ratio from balanced equation between Na and H2O is 1:1 (i.e., for every 1 mole of Na, 1 mole of H2O is required). Comparing the actual mole ratio (0.087 : 0.555) of Na to H2O with the stoichiometric ratio from the balanced equation, we can establish that Na (Sodium) is the limiting reactant since it has fewer moles in the reaction.

Computing The Mass of H2 Gas Produced

Given that Sodium is the limiting reactant, the mass of H2 gas produced will depend on the amount of Sodium present. From the balanced chemical equation, it's evident for every 2 moles of Na, 1 mole of H2 gas is produced. Hence, if 0.087 moles of Na is reacted, the amount of H2 produced in moles will be half of that, i.e. \( 0.087 / 2 = 0.0435 \, moles\). The mass of H2 produced can be calculated by multiplying the number of moles by H2's molar mass (roughly 2.02 g/mol), which yields: \( 0.0435 \, moles \times 2.02 \, g/mol = 0.088 \, g\).

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass where the total mass of reactants equals the total mass of products. To understand stoichiometry, one must grasp the concept of the mole, which is the standard unit for measuring the amount of substance in chemistry. A mole corresponds to Avogadro's number, approximately 6.022 x 10²³, of particles (atoms, molecules, ions, etc.).

In stoichiometry, chemical equations are used as recipes to determine the amounts of reactants and products involved. For example, in the given reaction, stoichiometry allows us to find out how much hydrogen gas is produced when sodium reacts with water. We achieve this by using the balanced chemical equation as a ratio to compare the moles of reactants we have to those required by the equation. By identifying the limiting reactant, stoichiometry can predict the mass of products formed in the reaction.

Single Displacement Reaction

A single displacement reaction, also known as a replacement reaction, occurs when an element reacts with a compound and takes the place of another element within that compound. In this type of reaction, a more reactive element displaces a less reactive element.

For instance, in the provided exercise, sodium (Na) displaces hydrogen (H) from water (H₂O), resulting in the formation of sodium hydroxide (NaOH) and hydrogen gas (H₂). This reaction follows the general pattern A + BC → B + AC, where A replaces B in the compound BC. These reactions are often exothermic, releasing energy in the form of heat or light.

Molar Mass Calculation

The molar mass of a substance is the mass of one mole of that substance and is expressed in grams per mole (g/mol). It is the sum of the atomic masses of all the atoms in a molecule as listed on the periodic table.

To calculate molar mass, one must identify each element present in the molecule and count the number of atoms of each element in the molecular formula. Then, the atomic mass of each element, measured in atomic mass units (amu), is multiplied by the number of atoms of that element in the molecule. Finally, all the resulting values are summed up to find the molar mass of the substance. Molar mass calculations are fundamental in the step-by-step solution because they allow the conversion between mass in grams and the amount of substance in moles.

Chemical Reaction Balancing

Balancing a chemical reaction involves making sure that the number of atoms of each element is the same on both the reactant and product sides of the equation. This is a requirement due to the Law of Conservation of Mass, which states that mass cannot be created or destroyed in a chemical reaction.

When balancing a reaction, one must place coefficients in front of the chemical formulas to ensure that the same number of atoms of each element are involved in the reactants and products. In the exercise, the reaction is balanced by placing a coefficient of 2 in front of Na, H₂O, NaOH, and H₂, indicating that two moles of sodium react with two moles of water to produce two moles of sodium hydroxide and one mole of hydrogen gas. Balancing is crucial for correctly applying stoichiometry and predicting the results of a chemical reaction.