Question

Consider the following unbalanced chemical equation for the combination reaction of sodium metal and chlorine gas: $$ \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{NaCl}(s) $$ What volume of chlorine gas, measured at STP, is necessary for the complete reaction of \(4.81 \mathrm{~g}\) of sodium metal?

Short answer

To completely react with 4.81 g of sodium metal at STP, 2.34 L of chlorine gas is necessary.

Step-by-step solution

Balance the chemical equation

Using coefficients to balance the given chemical equation, we get: \[ 2 \mathrm{Na}(s) + \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NaCl}(s) \]

Calculate the number of moles of sodium metal

We're given that the mass of sodium metal is 4.81 g. To find the number of moles, we'll use the molar mass of sodium: - Molar mass of sodium (Na) = 22.99 g/mol Using the formula, n = mass/molar_mass: \( n(\mathrm{Na}) = \frac{4.81 \,\mathrm{g}}{22.99\, \mathrm{g/mol}} \) \( n(\mathrm{Na}) = 0.209\, \mathrm{mol} \) So, we have 0.209 moles of sodium metal.

Determine the number of moles of chlorine gas required

From the balanced equation in Step 1, we can see that the mole ratio of Na to Cl2 is 2:1. This means that for every 2 moles of sodium, we need 1 mole of chlorine gas. Using the mole ratio, we can calculate the number of moles of Cl2 needed for the reaction: \( n(\mathrm{Cl_{2}}) = \frac{1}{2} \times n(\mathrm{Na}) \) \( n(\mathrm{Cl_{2}}) = \frac{1}{2} \times 0.209\, \mathrm{mol} \) \( n(\mathrm{Cl_{2}}) = 0.1045\, \mathrm{mol} \) So, 0.1045 moles of chlorine gas are required for the complete reaction.

Calculate the volume of chlorine gas at STP

At STP (standard temperature and pressure), 1 mole of any gas occupies 22.4 L. We can use this to calculate the volume of Cl2 gas required: \( V(\mathrm{Cl_{2}}) = n(\mathrm{Cl_{2}}) \times V(\mathrm{STP}) \) \( V(\mathrm{Cl_{2}}) = 0.1045\, \mathrm{mol} \times 22.4\,\mathrm{L/mol} \) \( V(\mathrm{Cl_{2}}) = 2.34\, \mathrm{L} \) Therefore, 2.34 L of chlorine gas are necessary for the complete reaction of 4.81 g of sodium metal at STP.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that involves quantifying the relationships between reactants and products in a chemical reaction. It is fundamental in ensuring that chemical equations are balanced, which means that the number of atoms for each element is the same on both the reactant and product sides of the equation.

This concept is applied in the given exercise by finding the balanced equation for the reaction between sodium and chlorine gas. The balanced equation shows that two moles of sodium react with one mole of chlorine gas to produce two moles of sodium chloride. Understanding stoichiometry is crucial because it allows us to find out how much reactant is needed to react completely with a given amount of another reactant, or how much product will form, based on the conservation of mass and the stoichiometric ratios.

Mole Concept

The mole concept is a way to count particles, such as atoms, molecules, and ions, by relating them to a quantity we can measure – mass. Avogadro's number (\(6.022 \times 10^{23}\) particles per mole) is a fundamental component, as it tells us how many particles are in one mole of a substance.

In the exercise, we are given the mass of sodium and need to find out how many particles (in moles) it represents. This is done by dividing the mass of sodium by its molar mass, thus converting grams into moles, a step that is vital because chemical equations are balanced in terms of moles, not grams. Using mole ratios from the balanced chemical equation then allows us to determine the amount of chlorine gas needed in moles.

Standard Temperature and Pressure

Standard Temperature and Pressure (STP) is a reference point used in chemistry to define a standard set of conditions for measurements, which is 0°C (273.15 K) for temperature and 1 atmosphere (atm) for pressure. These conditions are significant when considering the volume of gases, as gas volumes are highly dependent on temperature and pressure.

In the exercise, when we calculate the volume of chlorine gas needed for the reaction, we do so under the assumption that the gas is at STP. This allows us to use the standard molar volume of a gas to calculate the volume from the number of moles.

Molar Volume of a Gas

Molar volume is the volume occupied by one mole of a substance. For gases, the molar volume at STP is approximately 22.4 liters per mole. This is a direct application of Avogadro's law, which states that equal volumes of all gases at the same temperature and pressure contain the same number of particles (moles).

In the context of our exercise, knowing the molar volume of a gas at STP allows us to convert moles of chlorine gas into a volume. After determining the number of moles of chlorine gas required using stoichiometry and the mole concept, we multiply it by the molar volume to find out the space it will occupy at standard temperature and pressure.