# 11.5: Universal Gas Law

**At Grade**Created by: CK-12

Compressed gases provide vital fuels for industry and for homes and farms in rural areas.

### Universal Gas Law

The combined gas law,

Because different gases have different weights per molecule, including a term for mass of gas does not produce a consistent equation. If, however, we include a term expressing the number of moles of gas rather than its mass, we can produce a constant proportionality. A mole is a unit representing the number of atoms present. The letter **universal gas law**,

The unit term for

Pressure Units | Volume Units | Units for |
Units for |
Value of |

atm | liters | moles | Kelvin | 0.0821 L•atm/mol•K |

atm | milliliters | moles | Kelvin | 82.1 mL•atm/mol•K |

Since the product of (liters)(atm) can be converted to joules, we also have a value for **universal gas law constant** ** R **are

Most universal gas law problems are calculated at STP. STP stands for *standard temperature and pressure,* which is the most commonly calculated temperature and pressure value. STP is defined as 1.00 atm and 0°C, or 273 K.

### Examples

**Example 1**

Determine the volume of 1.00 mol of any gas at STP.

First isolate V from PV=nRT. Then plug in known values and solve.

For any gas at STP, one mole has a volume of 22.4 liters. This can be an extremely convenient conversion factor.

**Example 2**

A sample of oxygen gas occupies 10.0 liters at STP. How many moles of oxygen are in the container?

### Summary

- The universal gas law is
PV=nRT , whereP is pressure,V is volume,n is number of moles,R is the universal gas law constant, andT is the absolute temperature. - The value of
R varies depending on the units used forP andV . Two common values are0.0821 L⋅atm/mol⋅K andR=8.314 J/mol⋅K . - STP is standard temperature and pressure; 273 K and 1.00 atm.
- One mole of a gas at STP has a volume of 22.4 liters.

### Review

- The initial pressure in a helium gas cylinder is 30 atm. After many balloons have been blown up, the pressure in the cylinder has decreased to 6 atm while the volume and temperature remain the same. What fraction of the original amount of gas remains in the cylinder?
- Calculate the volume of 8.88 mol of helium gas at 20.0°C and 1.19 atm pressure.

### Explore More

Use this resource to answer the questions that follow.

- Why is it important to have values for R in kPa, atm, and mmHg?
- Why do the units of R include pressure, temperature, volume, and moles?

### Notes/Highlights Having trouble? Report an issue.

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### Image Attributions

- State the universal gas law.
- State the universal gas law constant, R.
- Given three of the four unknowns in the universal gas law, solve for the fourth.

## Concept Nodes:

**Universal gas law:**\begin{align*}PV = nRT \end{align*}**Universal gas law constant:**Denoted by \begin{align*}R\end{align*}, two common values are \begin{align*}0.0821 \ \text{L} \cdot \text{atm/mol} \cdot \text{K}\end{align*} and \begin{align*}8.314 \ \text{J/mol} \cdot \text{K}\end{align*}.

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