Determining the Number of Moles of Air Present in a Given Volume

Oct 13, 2025 by magicalceylontours.com 36 views

Determining the Number of Moles of Air Present in a Given Volume

Understanding the Ideal Gas Law

The Ideal Gas Law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas to the number of moles of gas present. The Ideal Gas Law formula is given by:

PV = nRT \, (R = 62.396 \, \text{L} \cdot \text{torr} / \text{mol} \cdot \text{K})

where:

$P$ is the pressure of the gas in torr
$V$ is the volume of the gas in liters
$n$ is the number of moles of gas present
$R$ is the gas constant, which is equal to $62.396 \, \text{L} \cdot \text{torr} / \text{mol} \cdot \text{K}$
$T$ is the temperature of the gas in Kelvin

Choosing the Correct Equation

To determine the number of moles of air present in a given volume, we need to use the Ideal Gas Law formula. However, we need to convert the temperature from Celsius to Kelvin, as the Ideal Gas Law requires temperature in Kelvin.

The temperature in Kelvin is given by:

T (\text{K}) = T (\text{°C}) + 273.15

Substituting the given values, we get:

T (\text{K}) = 17.0^{\circ} \text{C} + 273.15 = 290.15 \, \text{K}

Solving for the Number of Moles

Now that we have the temperature in Kelvin, we can substitute the given values into the Ideal Gas Law formula:

PV = nRT

Rearranging the equation to solve for $n$ , we get:

n = \frac{PV}{RT}

Substituting the given values, we get:

n = \frac{(750 \, \text{torr})(1.35 \, \text{L})}{(62.396 \, \text{L} \cdot \text{torr} / \text{mol} \cdot \text{K})(290.15 \, \text{K})}

Simplifying the equation, we get:

n = \frac{1012.5}{18151.3}

n = 0.0558 \, \text{mol}

Conclusion

In this article, we have determined the number of moles of air present in a given volume using the Ideal Gas Law formula. We have converted the temperature from Celsius to Kelvin and substituted the given values into the equation. We have solved for the number of moles and obtained a value of $0.0558 \, \text{mol}$ .

Key Takeaways

The Ideal Gas Law formula is a fundamental concept in chemistry that describes the behavior of ideal gases.
The Ideal Gas Law formula is given by $PV = nRT$ , where $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the number of moles of gas present, $R$ is the gas constant, and $T$ is the temperature of the gas.
To determine the number of moles of air present in a given volume, we need to use the Ideal Gas Law formula and convert the temperature from Celsius to Kelvin.
The number of moles of air present in a given volume can be calculated using the equation $n = \frac{PV}{RT}$ .

References

Atkins, P. W. (2010). Physical Chemistry. Oxford University Press.
Chang, R. (2010). Physical Chemistry for the Biosciences. University Science Books.
Levine, I. N. (2014). Physical Chemistry. McGraw-Hill Education.

Further Reading

For more information on the Ideal Gas Law, see the article "The Ideal Gas Law: A Fundamental Concept in Chemistry".
For more information on the gas constant, see the article "The Gas Constant: A Fundamental Constant in Chemistry".
For more information on the temperature conversion, see the article "Temperature Conversion: Celsius to Kelvin".