Calculate the number of moles and molecules of ammonia (NH3) in a volume of 67.2 dm³ of it measured at STP.
Understand the Problem
The question is referring to a chemistry exercise that involves calculating the number of moles and molecules of ammonia given a specific volume at standard temperature and pressure (STP). The user seems to be looking for guidance on how to approach this type of calculation.
Answer
3 moles of ammonia corresponds to approximately \( 1.81 \times 10^{24} \) molecules.
Answer for screen readers
The number of moles of ammonia is 3 moles, and the number of molecules is approximately ( 1.81 \times 10^{24} ) molecules.
Steps to Solve
- Identify Given Information
We know the volume of ammonia ($NH_3$) is 67.2 dm³ and the molar volume of a gas at STP is 22.4 L/mol.
- Convert Volume to Moles
To find the number of moles of ammonia, we use the formula:
$$ n = \frac{\text{Volume of gas}}{\text{Molar volume of gas}} $$
Substituting the known values:
$$ n = \frac{67.2 , \text{dm}^3}{22.4 , \text{dm}^3/\text{mol}} $$
- Calculate Moles
Perform the calculation:
$$ n = \frac{67.2}{22.4} = 3 , \text{mol} $$
This tells us there are 3 moles of ammonia.
- Calculate Number of Molecules
Now, to find the number of molecules, use Avogadro's number:
$$ \text{Number of molecules} = n \times 6.022 \times 10^{23} $$
Substituting in the number of moles:
$$ \text{Number of molecules} = 3 \times 6.022 \times 10^{23} $$
- Perform Calculation for Molecules
Now calculate the number of molecules:
$$ \text{Number of molecules} = 18.066 \times 10^{23} $$
This simplifies to:
$$ \text{Number of molecules} = 1.8066 \times 10^{24} $$
The number of moles of ammonia is 3 moles, and the number of molecules is approximately ( 1.81 \times 10^{24} ) molecules.
More Information
Ammonia ($NH_3$) is commonly used in various industrial applications, including fertilizers and cleaning solutions. Understanding moles and molecules is crucial in chemistry for quantifying substances.
Tips
- Misplacing the decimal: Be careful with the division by the molar volume; ensure you correctly place the decimal when performing the calculation.
- Forgetting to convert units: Always check that your units match (e.g., dm³ to L) before calculations.
