You Breathe In 6.0 L Of Pure Oxygen At 298 K And 1000 KPa To Fill Your Lungs. How Many Moles Of Oxygen Did You Take In?Use The Ideal Gas Law: P V = N R T PV = NRT P V = N RT Where R = 8.31 L ⋅ KPa / Mol ⋅ K R = 8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} R = 8.31 L ⋅ KPa / Mol ⋅ K .A. 0.05

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the equation $PV = nRT$, where $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the number of moles of the gas, $R$ is the gas constant, and $T$ is the temperature of the gas in Kelvin.

Given Values

In this problem, we are given the following values:

• Volume of oxygen: 6.0 L
• Temperature: 298 K
• Pressure: 1000 kPa
• Gas constant: $R = 8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K}$

Applying the Ideal Gas Law

To calculate the number of moles of oxygen in the lungs, we can rearrange the ideal gas law equation to solve for $n$:

$n = \frac{PV}{RT}$

Substituting the given values, we get:

$n = \frac{(1000 \, \text{kPa})(6.0 \, \text{L})}{(8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K})(298 \, \text{K})}$

Calculating the Number of Moles

Now, let's perform the calculation:

$n = \frac{(1000 \, \text{kPa})(6.0 \, \text{L})}{(8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K})(298 \, \text{K})}$

$n = \frac{6000}{2474.58}$

$n \approx 2.43$

Conclusion

Therefore, the number of moles of oxygen in the lungs is approximately 2.43 moles.

Discussion

This calculation demonstrates the application of the ideal gas law to a real-world scenario. The ideal gas law is a powerful tool for understanding the behavior of gases and can be used to calculate various properties of gases, such as pressure, volume, and temperature.

Limitations

It's worth noting that the ideal gas law assumes that the gas is an ideal gas, which is not always the case in real-world scenarios. In reality, gases can exhibit non-ideal behavior due to intermolecular forces and other factors. However, the ideal gas law provides a useful approximation for many situations and can be used as a starting point for more complex calculations.

Real-World Applications

The ideal gas law has numerous real-world applications in fields such as chemistry, physics, engineering, and biology. Some examples include:

• Calculating the pressure of a gas in a container
• Determining the volume of a gas at a given temperature and pressure
• Understanding the behavior of gases in chemical reactions
• Modeling the behavior of gases in biological systems, such as the lungs

Conclusion

Q: What is the ideal gas law?

A: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is expressed by the equation $PV = nRT$, where $P$ is the pressure of the gas, $V$ is the volume of the gas, $n$ is the number of moles of the gas, $R$ is the gas constant, and $T$ is the temperature of the gas in Kelvin.

Q: What is the gas constant (R)?

A: The gas constant (R) is a physical constant that relates the pressure, volume, and temperature of a gas. It is typically denoted by the symbol R and has a value of approximately 8.31 L·kPa/mol·K.

Q: What is the difference between pressure and volume?

A: Pressure (P) is the force exerted by a gas on its container, measured in units such as pascals (Pa) or kilopascals (kPa). Volume (V) is the amount of space occupied by a gas, measured in units such as liters (L) or cubic meters (m³).

Q: How is the ideal gas law used in real-world applications?

A: The ideal gas law has numerous real-world applications in fields such as chemistry, physics, engineering, and biology. Some examples include:

• Calculating the pressure of a gas in a container
• Determining the volume of a gas at a given temperature and pressure
• Understanding the behavior of gases in chemical reactions
• Modeling the behavior of gases in biological systems, such as the lungs

Q: What are some limitations of the ideal gas law?

A: The ideal gas law assumes that the gas is an ideal gas, which is not always the case in real-world scenarios. In reality, gases can exhibit non-ideal behavior due to intermolecular forces and other factors. However, the ideal gas law provides a useful approximation for many situations and can be used as a starting point for more complex calculations.

Q: How can I calculate the number of moles of a gas using the ideal gas law?

A: To calculate the number of moles of a gas using the ideal gas law, you can rearrange the equation to solve for n:

$n = \frac{PV}{RT}$

Substitute the given values for P, V, R, and T, and perform the calculation to find the number of moles.

Q: What is the relationship between temperature and the ideal gas law?

A: Temperature (T) is an important variable in the ideal gas law, as it affects the behavior of the gas. The ideal gas law assumes that the temperature is constant, but in reality, temperature can vary and affect the behavior of the gas.

Q: Can I use the ideal gas law to calculate the pressure of a gas?

A: Yes, you can use the ideal gas law to calculate the pressure of a gas. Rearrange the equation to solve for P:

$P = \frac{nRT}{V}$

Substitute the given values for n, R, T, and V, and perform the calculation to find the pressure.

Q: What is the significance of the ideal gas law in chemistry and physics?

A: The ideal gas law is a fundamental concept in chemistry and physics that describes the behavior of gases under various conditions. It has numerous real-world applications and is used to calculate various properties of gases, such as pressure, volume, and temperature.