The combined gas law combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation. It is used to calculate the relationship between the pressure, volume, and temperature of a fixed amount of gas.
Understanding the Combined Gas Law
The combined gas law can be expressed in a formula that states:
PV / T = k
Where:
- P = Pressure
- V = Volume
- T = Temperature (in Kelvin)
- k = a constant value
This formula shows that the ratio of PV/T for a fixed amount of gas remains constant.
Calculating Changes Using Combined Gas Law
The combined gas law is most useful when examining how changes in conditions affect a gas. It allows us to compare two sets of conditions, before and after. The formula used for this is:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
- P₁= Initial Pressure
- V₁= Initial Volume
- T₁= Initial Temperature (in Kelvin)
- P₂= Final Pressure
- V₂= Final Volume
- T₂= Final Temperature (in Kelvin)
Steps to Use the Combined Gas Law
Here is how to utilize the formula:
- Identify the known and unknown values: Understand which values of P, V, and T are given in the problem and what value you are trying to calculate.
- Ensure Consistent Units: Make sure your pressure, volume and temperature measurements use consistent units, this is crucial for obtaining the correct answer. Temperature should be in Kelvin.
- Rearrange the formula: Algebraically manipulate the formula to solve for the unknown variable.
- Substitute known values: Plug in the known values into your rearranged formula.
- Solve: Do the math to calculate your final answer.
Example
Let's say we have 2 liters of gas at 300 K and 1 atm of pressure. If we increase the temperature to 350 K and the pressure to 1.5 atm, what would the new volume be?
Using the formula: (P₁V₁) / T₁ = (P₂V₂) / T₂
- P₁ = 1 atm
- V₁ = 2 L
- T₁ = 300 K
- P₂ = 1.5 atm
- T₂ = 350 K
Substitute the values into the formula and solve for V₂:
(1 atm * 2 L) / 300 K = (1.5 atm * V₂) / 350 K
V₂= (1 atm 2 L 350 K) / (300 K * 1.5 atm)
V₂= 1.56 L
Thus, the new volume of the gas would be approximately 1.56 liters.
Key Considerations
- Always convert temperature measurements to Kelvin before using the combined gas law. To convert from Celsius to Kelvin, use the formula: K = °C + 273.15.
- The combined gas law is an ideal gas law and does not work accurately under very high pressures or very low temperatures.
- The combined gas law applies to a fixed amount of gas. If you add or remove gas, this law will not apply.
- Make sure that all pressure units are the same before using them in the formula. Similarly, ensure all volume units are the same.
By applying the combined gas law correctly, you can determine how gas behavior will be impacted by changes in pressure, volume, and temperature.
