Equation For Combined Gas Law

Combined Gas Police force

Apr 30, 2022

The combined gas law defines the relationship betwixt pressure level, temperature, and book. It is derived from three other names gas laws, including Charles' police force, Boyle'south law, and Gay-Lussac's law. Below we explicate the equation for the police force, how information technology is derived, and provide practice problems with solutions.

The Combined Gas Law

The combined gas police relates pressure level, temperature, and volume when everything else is held constant (mainly the moles of gas, n). The most common form of the equation for the combined gas police force is as follows:

P is the pressure of the gas. T is the temperature of the gas. V is the book of the gas. And k is a constant. The verbal value of k volition depend on the moles of gas.

The combined gas law is likewise often written equally two dissimilar time points. That is:

Derivation of other form of the combined gas law

Both chiliad'southward are the same value and therefore can be set equal to each other. Resulting in the below equation:

The human relationship of the combined gas law works as long as the gasses act every bit ideal gasses. More often than not, this will exist truthful when the temperature is loftier and pressure is low. You lot can larn more about what makes a gas an ideal gas in the commodity 'The Platonic Gas Law'.

Derivation of the Combined Gas Law

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

Charle's law gives the relationship between volume and temperature. That is V/T = k. Boyle'south constabulary tells us that P*Five =one thousand. And finally, Gay-Lussac'southward law tells the states that P*T =yard.

Charles' law, Boyle's law and Gay-Lussac's law combined to make the combine gas law

When all these relationships are combined into 1 equation, we get the combined gas police.

When the combined gas law is expanded and the moles of gas (n) are not held constant, yous get the platonic gas law. You can also 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 law, that would happen by holding the moles of gas (n) constant.

Example Problem one

Suppose y'all accept 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 two.1L. What is the pressure of the sample now?

Solution:

Here nosotros are looking at two different states. The original state with subscript ane, and the second state with subscript 2. Outset, write out the variables we know:

V₁ = 2 Fifty

T₁ = 303 Chiliad

P_one = 760 mmHg

V_two =two.one L

T₂ = 340 K

P₂ =?

We know all the variables except P₂. Nosotros can too tell we are looking at a before and after land, and then we desire to use the post-obit equation.

Next, we rearrange the equation so information technology is solving for P₂. First, multiply each side by T₂.

Rearrange the formula in the example problem

And then dissever each side past V₂.

Rearrange and solve the practice problem

Now we plug in the variables we know and solve.

Solution to the practice problem for combined gas law

Our final force per unit area is 812 mmHg. Also discover that all the units cancel except the units for force per unit area.

Example Trouble ii

You collect a gas at 620 mmHg and 177 M. At the time of collection, information technology takes up a volume of ane.3 Fifty. What volition the volume of the gas exist when it moves to standard temperature and pressure?

Solution:

Here we are looking at 2 different states of the gas, state 1 and state two. Therefore we volition use the following form of the combined gas police force.

The offset step is to determine the variables we know. Pressure, temperature, and book are given for the original country one. And pressure level and temperature are given for land 2 because standard temperature and force per unit area are defined equally 760 mmHg and 273K. The only variable we don't know is volume 2, which is what we demand to solve for.

T_i = 177 K

P₁ = 620 mmHg

V_ane = ane.3 L

T₂ = 273 K

P₂ = 760 mmHg

V_two =?

To brand the math simpler, permit us rearrange the equation to solve for V₂ before plugging in values. To do this, we multiply both sides by T₂ and and then divide by P₂.