Question

A sample of hydrogen fluoride gas occupies $1250\mathrm{mL}$ at STP. What is the pressure in $\mathrm{mm}\mathrm{Hg}$ if the volume is $255\mathrm{mL}$ at ${300}^{\circ }\mathrm{C}?$

Short answer

The pressure is approximately 7686.93 mm Hg.

Step-by-step solution

Understand the Variables

First, identify the conditions given in the problem. At STP (Standard Temperature and Pressure), the initial volume $V_1$ is $1250\text{ mL}$, the initial temperature $T_1$ is $273.15\text{ K}$, and the initial pressure $P_1$ is $1\text{ atm}$ which equals $760\text{ mm Hg}$. The final volume $V_2$ is $255\text{ mL}$ and the final temperature $T_2$ is ${300}^{\circ }\text{ C}$, which must be converted to Kelvin: $T_2=300+273.15=573.15\text{ K}$. We need to find the final pressure $P_2$.

Apply the Combined Gas Law

The Combined Gas Law $$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$$We will rearrange this equation to solve for $P_2$:$$P_2=\frac{P_1{V}_1{T}_2}{T_1{V}_2}$$

Plug in the Known Values

Substitute the values from Step 1 into the equation:$$P_2=\frac{760\text{ mm Hg}\times 1250\text{ mL}\times 573.15\text{ K}}{273.15\text{ K}\times 255\text{ mL}}$$

Calculate the Result

Perform the arithmetic:$$P_2=\frac{535287875\text{ mm Hg mL K}}{69653.25\text{ mL K}}\approx 7686.93\text{ mm Hg}$$Hence, the final pressure $P_2$ is approximately $7686.93\text{ mm Hg}$.

Key concepts

Standard Temperature and Pressure

In the world of gases, understanding their behavior under different conditions is crucial. Standard Temperature and Pressure, often abbreviated as STP, is a reference point used in chemistry to provide a common temperature and pressure. At STP, the temperature is defined as 0°C, which is equivalent to 273.15 Kelvin (K), and the pressure is 1 atmosphere (atm). This is also equal to 760 millimeters of mercury (mm Hg). When solving gas law problems, defining initial conditions at STP helps to simplify calculations since you have a standardized base to start from. In our problem, the initial conditions of the gas sample at STP provide a straightforward starting point to use the Combined Gas Law for solving the new conditions of pressure or volume at different temperatures.

pressure conversion

Pressure conversion is an essential skill when dealing with gas law problems, particularly because pressure can be measured in various units. Common units include atmospheres (atm), millimeters of mercury (mm Hg), and Pascals (Pa). In our exercise, pressure was initially provided in atm (1 atm), but it needed to be converted to mm Hg, since the question asked for pressure in these units. Since 1 atm is equivalent to 760 mm Hg, this conversion was straightforward. Always ensure you understand which unit of pressure is required for your calculations. Use conversions if necessary to keep your equations consistent, which is crucial for the calculations to be correct.

temperature conversion

When solving gas law problems, accurate temperature measurement is crucial because temperature directly affects the volume and pressure of a gas. The Kelvin scale is the absolute temperature scale used in all gas law calculations. To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature.
In our example, the final temperature was 300°C. By adding 273.15, we arrived at a final temperature of 573.15 K. Always make sure to convert Celsius to Kelvin for these types of problems, as using the wrong scale can lead to incorrect results.

gas law problems

Gas law problems typically involve using relationships between pressure, volume, temperature, and sometimes the number of gas molecules. The Combined Gas Law is particularly useful because it combines Charles's Law, Boyle's Law, and Gay-Lussac's Law into one convenient formula: $$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$$ This formula allows you to solve for one unknown quantity when the others are known.
In our exercise, we used the Combined Gas Law to find the final pressure of a gas sample after a change in volume and temperature.
The steps were straightforward: Convert all measurements to the correct units, plug those values into the formula, rearrange to solve for the unknown, which was the final pressure in this case, and then calculate. Understanding these basic gas law concepts and how to apply them to solve problems is fundamental for success in chemistry.