Question

Lithium reacts with nitrogen gas according to the reaction: $$ 6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{~N}(s) $$ What mass of lithium (in g) reacts completely with \(58.5 \mathrm{~mL}\) of \(\mathrm{N}_{2}\) gas at \(\mathrm{STP} ?\)

Short answer

Approximately 1.34 g of lithium reacts completely with 58.5 mL of N2 gas at STP.

Step-by-step solution

Determine moles of nitrogen gas

Use the ideal gas law at standard temperature and pressure (STP, where 1 mole of any gas occupies 22.4 L) to calculate moles of nitrogen gas (N2). The volume of N2 is 58.5 mL, which we first convert to liters (58.5 mL = 0.0585 L). The number of moles is then calculated using the formula: moles = volume in liters / 22.4 L/mol.

Determine moles of lithium

From the balanced chemical equation, 1 mole of N2 gas reacts with 6 moles of Li. Use the ratio from the balanced chemical equation (6 moles Li : 1 mole N2) to calculate the moles of lithium required for the reaction.

Calculate the mass of lithium

Convert the moles of lithium to grams using its molar mass (6.94 g/mol). The formula to use is: mass = moles * molar mass.

Key concepts

Ideal Gas Law

The ideal gas law is a crucial concept in chemistry that relates the pressure, volume, temperature, and the amount of gas in moles. It is usually written in the form of the equation:
\[PV = nRT\]
where \(P\) is the pressure of the gas, \(V\) is the volume, \(n\) is the number of moles of the gas, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. At Standard Temperature and Pressure (STP), the volume occupied by one mole of an ideal gas is 22.4 liters, and the temperature is typically considered to be 273.15 K. In the context of the given exercise, we use this law to determine the amount of nitrogen gas in moles from its volume at STP. Understanding the ideal gas law is essential for stoichiometry problems where gas reactions occur under known pressure and temperature conditions.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is a bridge between the mass of a material and the amount of substance (in moles). Every chemical element has a specific molar mass, which can be found on the periodic table. For example, lithium (Li) has a molar mass of 6.94 g/mol.
Molar mass is vital when converting between moles and grams in chemical reactions. To find the mass that corresponds to a given number of moles, you multiply the number of moles by the molar mass. This concept is essential when we want to determine the mass of reactants or products in a chemical reaction, as is the case in our exercise where we calculate the mass of lithium needed to react with a given volume of nitrogen gas.

Balanced Chemical Equations

Balanced chemical equations are central to understanding chemical reactions. They show the reactants and products involved in a reaction and the proportions in which they react and are formed. In a balanced equation, the number of atoms for each element is the same on both sides of the reaction, preserving mass and conforming to the law of conservation of mass.
In our exercise, the reaction between lithium (Li) and nitrogen gas (N2) is represented by the equation: \[6 \mathrm{Li}(s) + \mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3}\mathrm{N}(s)\]
This tells us that six lithium atoms react with one nitrogen molecule to produce two units of lithium nitride (Li3N). The ratio of lithium to nitrogen gas is 6:1, meaning that for every mole of nitrogen gas, six moles of lithium are required. Balancing equations is crucial for determining the stoichiometry of a reaction, which allows us to calculate the amount of reactants needed or products formed.

Moles to Grams Conversion

The conversion of moles to grams is a fundamental aspect of stoichiometry, allowing chemists to measure out or predict the mass of substances required or produced in a chemical reaction. The process utilizes the molar mass of a substance as the conversion factor.
To convert moles to grams, you simply multiply the number of moles by the molar mass of the substance. The equation used is: \[\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}\]
For instance, in our exercise problem, after determining the moles of lithium required to react with nitrogen gas, we use lithium’s molar mass to find out the corresponding mass in grams. This conversion is the final step to knowing how much of a solid reactant to use when the reactant or product of a chemical reaction is a gas, as often encountered in laboratory or industrial settings.