Question

What volume in milliliters will 0.00922 \(g\) of \(H_{2}\) gas occupy at STP?

Short answer

The 0.00922 g of H₂ gas will occupy 102 mL at STP.

Step-by-step solution

Recall molar volume of a gas at STP

The molar volume is defined as the volume occupied by one mole of a substance at a specified temperature and pressure. At STP (Standard Temperature and Pressure: 0°C and 1 atm), the molar volume of any ideal gas is approximately 22.4 L/mol or 22,400 mL/mol.

Determine the molar mass of H₂ gas

To convert the given mass of H₂ gas into moles, we will need the molar mass of H₂. The molecular formula of hydrogen gas (H₂) consists of 2 Hydrogen atoms. The molar mass of hydrogen gas is: Molar mass of H₂ = (2 x atomic mass of H) = 2 x 1.01 g/mol = 2.02 g/mol

Convert the given mass of H₂ gas into moles

Now, we'll use the molar mass of H₂ to convert the mass (0.00922 g) into moles: moles of H₂ = (mass of H₂) / (molar mass of H₂) moles of H₂ = \( \frac{0.00922 \, g}{2.02 \, g/mol} \)

Calculate the moles of H₂ gas

Perform the calculation to find the moles of H₂ gas: moles of H₂ = \( \frac{0.00922 \, g}{2.02 \, g/mol} \)= 0.00456 mol

Determine the volume of H₂ gas at STP

We'll multiply the moles of H₂ by the molar volume at STP to obtain the volume occupied by the gas: Volume = (moles of H₂) x (molar volume at STP) Volume = (0.00456 mol) x (22,400 mL/mol)

Calculate the volume of H₂ gas

Perform the calculation to find the volume occupied by 0.00922 g of H₂ gas at STP: Volume = (0.00456 mol) x (22,400 mL/mol) = 102 mL The 0.00922 g of H₂ gas will occupy 102 mL at STP.

Key concepts

Molar Mass

The molar mass of a substance is a fundamental concept in chemistry. It is the mass of one mole of a particular substance. In simpler terms, it tells us the weight of a given amount of molecules or atoms, measured in grams per mole (g/mol). Understanding molar mass is crucial because it helps in converting the amount of a substance from grams to moles, and vice versa.
To find the molar mass of a compound, you need to sum up the atomic masses of all atoms in its formula. For example, in the case of hydrogen gas (H₂), which consists of two hydrogen atoms, we calculate the molar mass by doubling the atomic mass of hydrogen, resulting in 2.02 g/mol.
This transformation is essential when you need to handle chemical equations or determine the volume of gases using the ideal gas law.

STP (Standard Temperature and Pressure)

STP, or Standard Temperature and Pressure, is a widely used fixed set of conditions in gas calculations in chemistry, defined as 0°C (273.15 K) and 1 atm pressure. These conditions serve as a reference point, allowing scientists to compare and predict the behavior of gases.

• At STP, gases have consistent molar volumes, which greatly simplifies calculations.
• The universally accepted molar volume at STP for an ideal gas is 22.4 liters per mole, or 22,400 milliliters per mole.

By establishing STP, we can have a standard framework to predict the volume gases will occupy. This regularity makes it easier to explore concepts of gases in educational settings and is vital for calculations involving molar volume and gas stoichiometry.

Ideal Gas

The concept of an ideal gas is a theoretical model used to simplify the study of gas behaviors under various conditions. An ideal gas is characterized by two main assumptions: the gas particles do not attract or repel each other, and they occupy no volume themselves.

• These assumptions are crucial for simplifying calculations, as they allow us to use straightforward equations like the ideal gas law.
• In reality, no gas is perfectly ideal, but under typical conditions (like STP), many gases behave closely enough to ideal for practical purposes.

Understanding ideal gases helps when dealing with problems related to gas volumes, pressure, and temperature. The ideal gas law, represented by the equation \( PV = nRT \), relates pressure (P), volume (V), amount of substance in moles (n), the ideal gas constant (R), and temperature (T) in Kelvin. This makes calculating properties of gases easy when any three of the variables are known.