Which Equation is Derived From the Combined Gas Law

The combined gas law defines the relationship between pressure, temperature, and volume. It is derived from three other names gas laws, including Charles’ law, Boyle’s police, and Gay-Lussac’s law. Beneath we explain the equation for the law, how it is derived, and provide practice problems with solutions.

The Combined Gas Law

The combined gas law relates pressure, temperature, and volume when everything else is held constant (mainly the moles of gas, n). The most common class of the equation for the combined gas police is every bit follows:

P is the pressure of the gas. T is the temperature of the gas. V is the volume of the gas. And k is a abiding. The exact value of k will depend on the moles of gas.

The combined gas constabulary is as well often written as 2 different time points. That is:

Both thou’due south are the same value and therefore can be ready equal to each other. Resulting in the below equation:

The relationship of the combined gas law works as long as the gasses act as ideal gasses. By and large, this will be true when the temperature is high and force per unit area is low. You lot tin can learn more about what makes a gas an platonic gas in the article ‘The Ideal Gas Police force’.

Derivation of the Combined Gas Police force

The combined gas law is derived from combining Charles’ Law, Boyle’south Police force, and Gay-Lussac’s Police force.

Charle’s law gives the human relationship between book and temperature. That is Five/T = k. Boyle’s police tells us that P*V =thou. And finally, Gay-Lussac’s law tells the states that P*T =g.

When all these relationships are combined into i equation, nosotros get the combined gas law.

When the combined gas law is expanded and the moles of gas (n) are not held constant, you get the ideal gas law. You tin besides work backwa from the ideal gas law to become the other gas laws by holding different variables constant. In the case of the combined gas constabulary, that would happen by property the moles of gas (n) constant.

Instance Problem 1

Suppose y’all have a sample of gas at 303K in a container with a volume of 2L and pressure of 760mmHg. The sample is moved to a temperature of 340 K and the volume increases slightly to 2.1L. What is the pressure of the sample at present?

Solution:

Here we are looking at two dissimilar states. The original state with subscript 1, and the 2d state with subscript 2. First, write out the variables nosotros know:

V_one
= 2 L

T₁
= 303 Yard

P_one
= 760 mmHg

Five_two
=two.ane L

T₂
= 340 Thou

P_ii
=?

We know all the variables except P₂. We can also tell we are looking at a earlier and after state, then nosotros want to use the post-obit equation.

Next, we rearrange the equation so it is solving for P₂. Outset, multiply each side past T₂.

Then divide each side by 5₂.

Now we plug in the variables we know and solve.

Our final pressure is 812 mmHg. Also detect that all the units cancel except the units for pressure.

Example Problem two

You collect a gas at 620 mmHg and 177 K. At the time of collection, information technology takes up a volume of one.iii L. What will the volume of the gas be when information technology moves to standard temperature and pressure?

Solution:

Hither we are looking at two dissimilar states of the gas, state 1 and country 2. Therefore we will use the following form of the combined gas police.

The showtime footstep is to determine the variables we know. Pressure, temperature, and volume are given for the original state i. And pressure and temperature are given for state 2 because standard temperature and pressure level are defined as 760 mmHg and 273K. The just variable nosotros don’t know is volume 2, which is what we need to solve for.

T₁
= 177 K

P₁
= 620 mmHg

5₁
= i.3 50

T_ii
= 273 Yard

P₂
= 760 mmHg

5_ii
=?

To make the math simpler, let us rearrange the equation to solve for V_ii
before plugging in values. To do this, we multiply both sides past T_ii
then dissever by P_two.

At present we plug in the values nosotros know and solve.

The new book of the gas is ane.6L. Then every bit the temperature and pressure of the gas increased, the book of the gas also increased.

Other Gas Laws

• Charles’ Law
• Boyle’s Law
• Gay-Lussac’s Law
• Ideal Gas Police
• Dalton’s Law
• Avogadro’s Law
• Henry’s Law