# Ideal Gas Law Ratios

Instructor: Michael Eckert

Michael has a Bachelor's in Environmental Chemistry and Integrative Science. He has extensive experience in working with college academic support services as an instructor of mathematics, physics, chemistry and biology.

The Ideal Gas Law is used primarily in chemistry. The formula is PV = nRT. We can use this in solving problems involving gases and solve the equation for any of the variables to find our unknown.

## The Ideal Gas Law

In this lesson, we will go over the Ideal Gas Law. We will learn how to solve for its variables and how to use the Ideal Gas Law Equation (PV = nRT) to derive proportions or ratios to solve for more specified variables or unknowns.

## Definition

The Ideal Gas law (PV = nRT) is an equation representing the state of a homogenous mixture of gas, which sets variables of that gas's pressure (P) times volume (V) equal to the amount in moles (n) of that gas multiplied by the ideal gas constant (R) multiplied by its temperature (T).

### Ideal Gas Law Variables

Pressure (P) can be set equal to nRT/V:

P = nRT / V.

Volume (V) can be set equal to nRT / P:

V = nRT / P

Moles (n) can be set equal to PV / RT:

n = PV / RT

The ideal gas constant (R) can be set equal to PV / nT:

R = PV / nT

Temperature (T) can be set equal to PV / nR:

T = PV / nR

Note again that PV = nRT is a state equation. P, V, and T are variables. They are variables in that they represent physical properties (pressure, volume, and temperature) of a gas at a specific state. The number of moles (n) may be held constant and the ideal gas constant (R) is a constant that can be found in chemistry books.

• Pressure (P) becomes dependent on the ratio of T / V, where P is directly proportional to T and indirectly proportional to V.
• Volume (V) is a dependent to T / P, where V is directly proportional to T and indirectly proportional to P.
• Temperature (T) is dependent to PV, being directly proportional to any changes in both P and V.

## Using the Ideal Gas Law:

### The Ideal Gas Law and a Particular State

Given PV = nRT for a gas at a specific state, we can, therefore, solve for any of its variables as illustrated above. For instance, if we had a gas at state 1:

P1 V1= nRT1

and we wanted to calculate

P1, V1 or T1

we would merely use the proportions as given above:

P1 = nRT1/ V1

V1= nRT1/ P1

T1= P1 V1 /nR

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