What Is The Temperature Of 0.750 Mol Of A Gas Stored In A $6,850 \, \text{mL}$ Cylinder At $2.21 \, \text{atm}$?Use $PV = NRT$ And $R = 0.0821 \frac{L \cdot \text{atm}}{\text{mol} \cdot K}$.A. 2.95 K B. 5.24 K

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Understanding the Ideal Gas Law

The ideal gas law, also known as the general gas equation, is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. The equation is given by:

PV = nRT

Where:

  • P is the pressure of the gas in atmospheres (atm)
  • V is the volume of the gas in liters (L)
  • n is the number of moles of the gas
  • R is the gas constant, which is equal to 0.0821 L·atm/mol·K
  • T is the temperature of the gas in Kelvin (K)

Given Information

We are given the following information:

  • n = 0.750 mol (number of moles of the gas)
  • V = 6,850 mL (volume of the gas in milliliters)
  • P = 2.21 atm (pressure of the gas in atmospheres)

Converting Volume from Milliliters to Liters

Before we can use the ideal gas law, we need to convert the volume from milliliters to liters. There are 1,000 milliliters in 1 liter, so we can convert the volume as follows:

V = 6,850 mL × (1 L / 1,000 mL) = 6.85 L

Using the Ideal Gas Law

Now that we have the volume in liters, we can use the ideal gas law to solve for the temperature of the gas. Plugging in the given values, we get:

P × V = n × R × T

2.21 atm × 6.85 L = 0.750 mol × 0.0821 L·atm/mol·K × T

15.04 L·atm = 0.0618 L·atm/K × T

T = 15.04 L·atm / 0.0618 L·atm/K

T = 243.4 K

Rounding to Two Significant Figures

Since the answer choices are given to two significant figures, we can round our answer to two significant figures as well:

T ≈ 240 K

Comparing to Answer Choices

Now that we have calculated the temperature of the gas, we can compare our answer to the answer choices:

  • A. 2.95 K
  • B. 5.24 K
  • C. 240 K

Our answer, 240 K, is closest to answer choice C.

Conclusion

In this problem, we used the ideal gas law to calculate the temperature of a gas stored in a cylinder. We converted the volume from milliliters to liters, plugged in the given values, and solved for the temperature. Our answer, 240 K, is closest to answer choice C.

Key Takeaways

  • The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas.
  • The equation is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
  • We can use the ideal gas law to solve for the temperature of a gas given the pressure, volume, and number of moles.
  • We can convert the volume from milliliters to liters by multiplying by 1 L / 1,000 mL.
  • We can round our answer to two significant figures if the answer choices are given to two significant figures.
    Q&A: Understanding the Ideal Gas Law =====================================

Frequently Asked Questions

Q: What is the ideal gas law?

A: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. The equation is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Q: What is the gas constant (R)?

A: The gas constant (R) is a value that is used in the ideal gas law equation. It is equal to 0.0821 L·atm/mol·K.

Q: How do I convert the volume from milliliters to liters?

A: To convert the volume from milliliters to liters, you can multiply by 1 L / 1,000 mL. For example, if the volume is 6,850 mL, you can convert it to liters by multiplying by 1 L / 1,000 mL, which gives you 6.85 L.

Q: How do I use the ideal gas law to solve for the temperature of a gas?

A: To use the ideal gas law to solve for the temperature of a gas, you can plug in the given values into the equation PV = nRT. For example, if the pressure is 2.21 atm, the volume is 6.85 L, the number of moles is 0.750 mol, and the gas constant is 0.0821 L·atm/mol·K, you can solve for the temperature (T) by rearranging the equation to get T = PV / (nR).

Q: What is the significance of the ideal gas law?

A: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. It is used to describe the behavior of gases and is a crucial tool in understanding many chemical and physical processes.

Q: What are some common applications of the ideal gas law?

A: The ideal gas law has many common applications in chemistry and physics, including:

  • Calculating the temperature of a gas given the pressure, volume, and number of moles
  • Determining the volume of a gas given the pressure, temperature, and number of moles
  • Understanding the behavior of gases in chemical reactions and physical processes
  • Designing and optimizing gas storage systems and equipment

Q: What are some common mistakes to avoid when using the ideal gas law?

A: Some common mistakes to avoid when using the ideal gas law include:

  • Failing to convert the volume from milliliters to liters
  • Using the wrong value for the gas constant (R)
  • Failing to plug in the correct values into the equation
  • Not rounding the answer to the correct number of significant figures

Conclusion

In this Q&A article, we have covered some of the most frequently asked questions about the ideal gas law. We have discussed the equation, the gas constant, and how to use the ideal gas law to solve for the temperature of a gas. We have also covered some common applications and mistakes to avoid when using the ideal gas law.