The Combined Gas Law is a cornerstone of thermodynamics and physical chemistry. This law unites three critical gas laws that describe the behavior of gases: Boyle’s Law, Charles’ Law, and Gay-Lussac’s Law. These laws examine how the volume, temperature, and pressure of a gas are interrelated when a certain amount of gas is kept constant. The Combined Gas Law is expressed by the equation:
$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$Where:This equation allows you to predict the behavior of a gas when it undergoes changes in pressure, temperature, or volume, as long as the number of gas particles remains constant.
Boyle's Law (1662)
Robert Boyle, an Irish physicist, was the
first to propose that for a given mass of gas at constant
temperature, the pressure is inversely proportional to the
volume. In other words, when the pressure of a gas increases,
its volume decreases, and vice versa. This was revolutionary
at the time, as it laid the groundwork for future discoveries
in gas behavior.
Boyle’s equation:
$P_1V_1 = P_2V_2 \quad \text{(at constant temperature)}$Charles' Law (1780s)
French scientist Jacques Charles later
discovered that when a gas is held at a constant pressure, its
volume is directly proportional to its temperature. As the
temperature increases, so does the volume, which Charles
observed by studying how hot air balloons rise. Charles’ work
paved the way for understanding the expansion of gases.
Charles’ equation:
$\frac{V_1}{T_1} = \frac{V_2}{T_2} \quad \text{(at constant pressure)}$Gay-Lussac's Law (1802)
Building on these laws, Joseph Louis Gay-Lussac,
another French physicist, found that the pressure of a gas is
directly proportional to its temperature when volume remains
constant. This was particularly important for early
thermodynamic studies, especially in closed systems where
volume can’t change.
Gay-Lussac’s equation:
$\frac{P_1}{T_1} = \frac{P_2}{T_2} \quad \text{(at constant volume)}$The Combined Gas Law, developed by uniting these three separate laws, is incredibly useful when more than one factor is changing at a time, such as in real-world scenarios like weather balloons, pressurized gas tanks, or any system where gases are compressed or expanded under changing conditions.
Fig. Screen Shot from CHEMIX School Gas
Equations - Combined Gas Law Calculator
The Combined Gas Law Calculator you’ve designed
is a practical tool to solve problems related to gas behavior when
multiple variables change. It allows users to input known values
for any five of the six variables (initial and final pressure,
volume, and temperature), and it will calculate the unknown value
for them. Here’s how it works:
Enter known values: Input five of the six values (for example, the initial pressure $P_1$, initial volume $V_1$, and so on). Ensure that the values are valid and in consistent units (for example, temperature should be in Kelvin).
Leave one field empty: Leave the field corresponding to the value you want to calculate blank. The calculator will use the Combined Gas Law to determine this unknown value.
Press Enter: Ensure that your cursor is in one of the text fields, then press Enter. The calculator will compute the missing value and display it in the previously empty field.
Auto-Erase Feature: Clicking on any field will erase its content, allowing you to insert new values without having to delete the previous data.
Cursor Position: The calculator will only compute the result if the cursor is focused on one of the input fields when you press Enter. So make sure the cursor is active in one of the fields before attempting a calculation.
This user-friendly tool is designed for quick and efficient calculations, making it ideal for students, engineers, or hobbyists dealing with gas laws in real-world applications