Question

A flask containing \(\mathrm{H}_{2}\) at \(0^{\circ} \mathrm{C}\) was sealed off at a pressure of 1 atm and the gas was found to weigh, \(4512 \mathrm{~g}\). Calculate the number of moles and the number of molecules of \(\mathrm{H}_{2}\) present.

Short answer

There are 2240 moles of H₂ gas and approximately \( 1.35 \times 10^{27} \) molecules of H₂ gas in the flask.

Step-by-step solution

Convert the weight of hydrogen gas to moles

To find the number of moles, we will use the molar mass of hydrogen gas (H₂). The molar mass of H₂ is approximately 2.016 g/mol. Number of moles (n) = mass / molar mass n = \( \frac{4512 \, g}{2.016 \, g/mol} \)

Calculate the number of moles

Now we can calculate the number of moles: n = \( \frac{4512 \, g}{2.016 \, g/mol} = 2240 \, mol \) There are 2240 moles of H₂ gas in the flask.

Calculate the number of molecules

Now we can use Avogadro's number (6.022 x 10²³) to find the number of molecules in the flask. Number of molecules = moles x Avogadro's number Number of molecules = \( 2240 \, mol \cdot 6.022 \times 10^{23} \, molecules/mol \)

Determine the number of H₂ molecules

Now we can determine the number of H₂ molecules present in the flask: Number of H₂ molecules = \( 2240 \, mol \cdot 6.022 \times 10^{23} \, molecules/mol = 1.35 \times 10^{27} \, molecules \) There are approximately \( 1.35 \times 10^{27} \) molecules of H₂ gas in the flask.

Key concepts

Avogadro's Number

Avogadro's number, named after scientist Amedeo Avogadro, is a fundamental constant used in chemistry to represent the number of constituent particles, usually atoms or molecules, in one mole of a substance. The approximate value of Avogadro's number is \(6.022 \times 10^{23}\) particles per mole. This constant is vital when converting between the number of particles and the amount of substance in moles.

Understanding Avogadro's number helps clarify the scale of chemical reactions at the molecular level. Since dealing with individual molecules on such a vast scale is virtually impossible, the mole concept, together with Avogadro's number, bridges the gap between microscopic and macroscopic amounts. For instance, if we say we have 1 mole of \(\mathrm{H}_{2}\) molecules, this means we have \(6.022 \times 10^{23}\) \(\mathrm{H}_{2}\) molecules. This conversion is essential in the problem we're exploring because it allows us to determine the sheer number of molecules from the weight of hydrogen gas provided.

Molar Mass

Molar mass is a property of a substance that tells us the mass of one mole of that substance. It is typically expressed in units of grams per mole (g/mol) and is calculated as the sum of the atomic masses of all atoms in a molecule. For example, the molar mass of water (\(\mathrm{H}_2\mathrm{O}\)) is the sum of the masses of two hydrogen atoms and one oxygen atom.

In our exercise, the molar mass of dihydrogen (\(\mathrm{H}_2\)) is approximately 2.016 g/mol. Knowing the molar mass allows us to convert from grams of a substance to moles, which is a necessary step when working with quantitative aspects of chemical equations. To find the moles (\