Liters to Moles Calculator

How to Calculate Liters to Moles (and vice versa)

Converting between liters and moles is a fundamental calculation in chemistry, especially when dealing with gases. This conversion relies on the ideal gas law, which describes the relationship between pressure, volume, temperature, and the number of moles of a gas.

What is the Formula?

The ideal gas law is expressed as:

\[ PV = nRT \]

Where:

• P = Pressure (in atmospheres, atm)
• V = Volume (in liters, L)
• n = Number of moles
• R = Gas constant (0.08206 L⋅atm⋅K^−1⋅mol^−1)
• T = Temperature (in Kelvin, K)

To convert from liters to moles, we rearrange the equation to solve for n:

\[ n = \frac{PV}{RT} \]

To convert from moles to liters, we rearrange the equation to solve for V:

\[ V = \frac{nRT}{P} \]

What are the calculation steps?

1. Ensure all units are correct (pressure in atm, volume in L, temperature in K)
2. Identify the known variables and the variable you want to calculate
3. Plug the known values into the appropriate formula
4. Solve the equation for the unknown variable

Example Calculation

Let's calculate the number of moles of a gas that occupies 5.0 L at 2.0 atm and 300 K:

Given:

• V = 5.0 L
• P = 2.0 atm
• T = 300 K
• R = 0.08206 L⋅atm⋅K^−1⋅mol^−1

Step 1: Identify the formula

We're calculating the number of moles, so we'll use: n = PV / RT

Step 2: Substitute the values

n = (2.0 atm * 5.0 L) / (0.08206 L⋅atm⋅K^−1⋅mol^−1 * 300 K)

Step 3: Solve the equation

n = 10 / 24.618 = 0.406 moles

Therefore, 5.0 L of the gas at 2.0 atm and 300 K contains 0.406 moles.

Diagram of Gas Laws

The following diagram illustrates the relationships between pressure, volume, temperature, and number of moles in the ideal gas law:

This diagram shows how the variables in the ideal gas law are interrelated. As one variable changes, the others must adjust to maintain the equality PV = nRT. For instance, if temperature increases while pressure remains constant, the volume must increase proportionally.