Question

How many moles are present in \(334 \mathrm{~L}\) of \(\mathrm{H}_{2}\) at STP?

Short answer

There are approximately 14.91 moles of H2.

Step-by-step solution

Identify Known Information

We are given the volume of the gas, which is 334 L of hydrogen (\( \text{H}_2\)) at Standard Temperature and Pressure (STP).

Understand STP Conditions

At Standard Temperature and Pressure (STP), one mole of any gas occupies a volume of 22.4 L.

Calculate Moles of Gas

Use the relationship between moles, volume, and the STP condition: \[ \text{Moles} = \frac{\text{Volume at STP}}{22.4 \text{ L}} \] Substitute the given volume: \[ \text{Moles} = \frac{334 \text{ L}}{22.4 \text{ L/mol}} = 14.91 \text{ moles}\]

Key concepts

Understanding Moles

The concept of a mole is a fundamental building block in chemistry that helps us quantify the amount of any substance. A mole is defined as exactly 6.022 x 10^{23} particles of a given substance, whether they are atoms, molecules, or ions. This number is known as Avogadro's number.

• The mole serves as a bridge between the atomic scale and the macroscopic scale.
• Using moles allows chemists to count particles by weighing them.

When dealing with gas, like hydrogen (\( \text{H}_2 \)), at standard laboratory conditions, moles are particularly useful for relating volumes to amounts. Whenever you're asked how many moles are present in a gas at STP, know that moles are at the heart of connecting volume measurements to molecular quantities.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, abbreviated as STP, is a convention used by scientists to ensure consistency while measuring gases. At STP, the temperature is set to 0 degrees Celsius (273.15 Kelvin) and the pressure is 1 atm (atmosphere).

• Under these conditions, one mole of an ideal gas occupies 22.4 liters.
• STP is a reference point to compare different gas behaviors and calculations.

STP makes it easier to predict how gases will occupy space and helps in making generalized calculations about gas volume that are useful in real-world applications, like estimating how a chemical reaction will proceed in a container.

Volume to Moles Conversion

Converting volume to moles is crucial in dealing with gases. At STP, the volume of a gas directly relates to the number of moles. For any ideal gas at STP, the conversion is straightforward using the ratio:\[\text{Moles} = \frac{\text{Volume at STP (in L)}}{22.4 \text{ L/mol}} \]When you have the volume of gas and need to find out how many moles it represents, divide the volume by 22.4 L (since 1 mole of gas at STP occupies 22.4 L).
For example, for 334 L of hydrogen gas, you use the formula above to calculate moles:\[\text{Moles of } \text{H}_2 = \frac{334 \text{ L}}{22.4 \text{ L/mol}} = 14.91 \text{ moles}\]This simple yet powerful conversion allows a chemist to easily interpret and predict reactions involving gases. It connects what's observed (in volume) to what's important (in molecular terms).