If 1.00 L of nitrogen gas is reacted with 3.0 L of fluorine gas, how many litres of nitrogen trifluoride gas will be produced?
Understand the Problem
The question is asking us to determine the volume of nitrogen trifluoride gas produced when 1.00 L of nitrogen gas reacts with 3.0 L of fluorine gas. We will use the stoichiometry of the reaction to find the result.
Answer
$2.00 \, \text{L}$
Answer for screen readers
The volume of nitrogen trifluoride gas produced is $2.00 , \text{L}$.
Steps to Solve
- Write the balanced chemical equation
First, we need to write and balance the chemical equation for the reaction between nitrogen gas ($\text{N}_2$) and fluorine gas ($\text{F}_2$) to form nitrogen trifluoride ($\text{NF}_3$).
The balanced equation is: $$ \text{N}_2 + 3\text{F}_2 \rightarrow 2\text{NF}_3 $$
- Determine the limiting reactant
Next, we need to identify the limiting reactant since it determines how much product can be formed.
From the balanced equation, the stoichiometry tells us that 1 volume of $\text{N}_2$ reacts with 3 volumes of $\text{F}_2$. We have 1.00 L of $\text{N}_2$ and 3.0 L of $\text{F}_2$.
We compare:
- For 1.00 L of $\text{N}_2$, we need $3 \times 1.00 , \text{L} = 3.00 , \text{L}$ of $\text{F}_2$.
- We have exactly 3.0 L of $\text{F}_2$, so both gases will react completely, and none is left over.
- Calculate the produced volume of nitrogen trifluoride
Since 1.00 L of $\text{N}_2$ will produce $2 \times 1.00 , \text{L} = 2.00 , \text{L}$ of $\text{NF}_3$ according to the balanced equation, we can calculate the total volume of the product.
- Final calculation for the volume of nitrogen trifluoride
The total volume of nitrogen trifluoride produced is: $$ \text{Volume of } \text{NF}_3 = 2 \text{ moles of } \text{NF}_3 \text{ from } 1 \text{ mole of } \text{N}_2 = 2 \operatorname{L} $$
The volume of nitrogen trifluoride gas produced is $2.00 , \text{L}$.
More Information
This problem demonstrates the principles of stoichiometry and the behavior of gases, particularly how to use the ideal gas law under standard conditions, where equal volumes of gases at the same temperature and pressure contain the same number of molecules.
Tips
- A common mistake is to forget to balance the chemical equation correctly, which can lead to incorrect volume calculations.
- Another mistake is to misidentify the limiting reactant, which can result in miscalculating the amount of product formed.
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