An ideal gas is contained in a cylinder with a volume of 5.0 ×10^2 mL at a temperature of 30 .^∘

step 1 We have 500 milliliters of gas at 710 Tor and 30 degrees Celsius. We are going to change the vol

An ideal gas is contained in a cylinder with a volume of 5.0...

An ideal gas is contained in a cylinder with a volume of $5.0 \times 10^{2} \mathrm{mL}$ at a temperature of $30 .^{\circ} \mathrm{C}$ and a pressure of $710.$ torr. The gas is then compressed to a volume of $25 \mathrm{mL}$ and the temperature is raised to $820 .^{\circ} \mathrm{C}$. What is the new pressure of the gas?

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Key Concepts

Combined Gas Law

The Combined Gas Law is a useful application of the Ideal Gas Law when the amount of gas remains constant. It relates the initial and final states of a gas by combining Boyle's Law, Charles's Law, and Gay-Lussac's Law into the equation (P1V1)/T1 = (P2V2)/T2. This law is pivotal for solving problems where pressure, volume, and temperature all change simultaneously.

Temperature Conversion

Temperature Conversion is a key concept in thermodynamics, particularly when using the Ideal Gas Law, because temperatures must be measured in Kelvin to ensure accurate calculations. Converting from Celsius to Kelvin is done by adding 273.15, a necessary step to maintain consistency and validity in gas law computations.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics expressed as PV = nRT, which relates the pressure (P), volume (V), number of moles (n), ideal gas constant (R), and temperature (T) of a gas. This law is essential for understanding how gases behave under changes in state variables and is widely used to solve problems involving gas expansions, compressions, and temperature changes.

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