A gas has a volume of 2.84 L at 1.00 atm and 0 °C. At what temperature does it have a volume of 7.50 L at 520 mmHg?

Verified step by step guidance

1. Identify the initial and final conditions of the gas: initial volume (V1) = 2.84 L, initial pressure (P1) = 1.00 atm, initial temperature (T1) = 0 °C, final volume (V2) = 7.50 L, final pressure (P2) = 520 mmHg.
2. Convert all units to be consistent: convert the initial temperature from Celsius to Kelvin using T(K) = T(°C) + 273.15, and convert the final pressure from mmHg to atm using the conversion factor 1 atm = 760 mmHg.
3. Use the combined gas law, which is $\frac{P_1\cdot V_1}{T_1}=\frac{P_2\cdot V_2}{T_2}$, to relate the initial and final states of the gas.
4. Rearrange the combined gas law to solve for the final temperature $T_2$: $T_2=\frac{P_2\cdot V_2\cdot T_1}{P_1\cdot V_1}$.
5. Substitute the known values into the equation and solve for $T_2$ in Kelvin.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict how a gas will behave under different conditions.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Mathematically, it can be expressed as V1/T1 = V2/T2. This principle is crucial for understanding how changes in temperature affect the volume of a gas, which is essential for solving the given problem.

Pressure Conversion

Pressure conversion is the process of changing pressure units from one system to another, such as from atmospheres (atm) to millimeters of mercury (mmHg). In this case, 1 atm is equivalent to 760 mmHg. Understanding how to convert between these units is necessary to apply the Ideal Gas Law and Charles's Law correctly in the context of the problem.