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. Step 1: Identify the gas law to use. Since the problem involves changes in pressure, volume, and temperature, use the combined gas law: $\frac{P_1}{V_1}/T_1=\frac{P_2}{V_2}/T_2$.
2. Step 2: Convert all given values to appropriate units. Ensure temperature is in Kelvin (K) by adding 273.15 to the Celsius value. Convert pressure from mmHg to atm using the conversion factor: $1$ atm = $760$ mmHg.
3. Step 3: Rearrange the combined gas law to solve for the unknown temperature, $T_2$: $T_2=\frac{P_2{V}_2{T}_1}{P_1{V}_1}$.
4. Step 4: Substitute the known values into the rearranged equation. Use the converted values for pressure, volume, and temperature. Ensure all units are consistent.
5. Step 5: Perform the calculation to find $T_2$. If needed, convert the result back to Celsius by subtracting 273.15 from the Kelvin temperature.

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.