Math Problem Statement

15.0 L of an ideal gas at 298 K and 3.36 atm are heated to 383 K with a new pressure of 6.00 atm. What is the new volume in liters?

Solution

This question is about the ideal gas law, where the gas changes its volume, temperature, and pressure. You can use the combined gas law, which is:

P1V1T1=P2V2T2\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Where:

  • P1P_1 = 3.36 atm (initial pressure)
  • V1V_1 = 15.0 L (initial volume)
  • T1T_1 = 298 K (initial temperature)
  • P2P_2 = 6.00 atm (final pressure)
  • T2T_2 = 383 K (final temperature)
  • V2V_2 = ? (final volume, to be calculated)

Let's solve for V2V_2:

V2=P1V1T2P2T1V_2 = \frac{P_1 V_1 T_2}{P_2 T_1}

I'll compute this now.The new volume (V2V_2) of the gas is approximately 10.80 liters.

Would you like more details on this calculation or have any questions?

Here are 5 related questions you might find helpful:

  1. How does temperature affect the volume of a gas at constant pressure?
  2. What happens to the volume of a gas if both pressure and temperature increase?
  3. Can you explain the ideal gas law and its assumptions?
  4. How do real gases deviate from ideal gas behavior under high pressure or low temperature?
  5. How would you calculate the amount of gas (in moles) given the volume, pressure, and temperature?

Tip: When using the combined gas law, ensure temperatures are always in Kelvin, as it directly relates to the kinetic energy of particles.

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Math Problem Analysis

Mathematical Concepts

Ideal Gas Law
Algebra
Proportions

Formulas

(P1 * V1) / T1 = (P2 * V2) / T2
V2 = (P1 * V1 * T2) / (P2 * T1)

Theorems

Combined Gas Law

Suitable Grade Level

Grades 10-12