Question

What mass of hydrogen contains the same number of atoms as \(7.00 \mathrm{g}\) of nitrogen?

Short answer

The mass of hydrogen that contains the same number of atoms as \(7.00 \mathrm{g}\) of nitrogen is approximately \(1.008 \mathrm{g}\).

Step-by-step solution

Calculate the number of moles of nitrogen in 7.00 g

To find the number of moles of nitrogen in 7.00 g, we use the formula: Number of moles = \(\frac{mass}{molar~mass}\) Number of moles of Nitrogen = \(\frac{7.00 \mathrm{g}}{14.01 \mathrm{g/mol}}\)

Calculate the number of atoms of nitrogen present

Now that we have the number of moles of nitrogen, we can find the number of atoms by using Avogadro's number: Number of atoms = (Number of moles) \(\times\) (Avogadro's number) Number of atoms of Nitrogen = \(\frac{7.00 \mathrm{g}}{14.01 \mathrm{g/mol}} \times 6.022 \times 10^{23} \mathrm{atoms/mol}\)

Calculate the number of moles of hydrogen

Since the number of atoms of hydrogen is equal to the number of atoms of nitrogen, we can find the number of moles of hydrogen using: Number of moles of Hydrogen = \(\frac{Number~of~atoms~of~Hydrogen}{Avogadro's~number}\) Number of moles of Hydrogen = \(\frac{(\frac{7.00 \mathrm{g}}{14.01 \mathrm{g/mol}} \times 6.022 \times 10^{23} \mathrm{atoms/mol})}{6.022 \times 10^{23} \mathrm{atoms/mol}}\)

Calculate the mass of hydrogen required

Finally, we can find the mass of hydrogen using the molar mass of hydrogen and the number of moles calculated above: Mass of Hydrogen = (Number of moles of Hydrogen) \(\times\) (Molar mass of Hydrogen) Mass of Hydrogen = \(\frac{(\frac{7.00 \mathrm{g}}{14.01 \mathrm{g/mol}} \times 6.022 \times 10^{23} \mathrm{atoms/mol})}{6.022 \times 10^{23} \mathrm{atoms/mol}} \times 1.008 \mathrm{g/mol}\) Calculate the value of the mass of hydrogen to get the final answer.

Key concepts

Molar Mass

When you work with chemical reactions, it's crucial to know how much of each substance is involved. This is where molar mass comes into play. Molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). This number tells us how many grams are present in one mole of a substance and it is essential for converting between the mass of a substance and the amount of substance in moles.

For example, the molar mass of hydrogen (H) is about 1.008 g/mol, whereas for nitrogen (N), it is approximately 14.01 g/mol. To calculate the molar mass of a compound, you would add up the molar masses of all the individual elements according to their proportions in the compound. Knowing the molar mass allows for precise chemical calculations, which are indispensable for experiments and industry applications.

Avogadro's Number

A cornerstone concept in chemistry is Avogadro's number. This incredibly large constant, approximately 6.022 x 10²³, represents the number of atoms, ions, or molecules in one mole of a substance. It's named after Amedeo Avogadro, an Italian scientist who contributed significantly to molecular theory.

This constant allows chemists to count particles by weighing them. Since we cannot count each atom or molecule individually due to their miniscule size, Avogadro's number provides a way to translate between the macroscopic world of grams and the microscopic world of atoms.

Moles to Grams Calculation

One of the fundamental skills in chemical calculations is the ability to convert moles to grams and vice versa. This is done by using the molar mass of the substance in question. The formula is quite simple: mass (g) = number of moles × molar mass (g/mol).

If you're given the mass of a substance and need to find the number of moles, you would rearrange the formula to: number of moles = mass (g) / molar mass (g/mol). This process is pivotal in stoichiometry since it provides a bridge between the mass of a substance and the number of particles it contains.

Chemical Calculations

Chemical calculations often involve a series of conversions and require a clear understanding of the relationships between units like moles, grams, and the number of particles. These calculations are the backbone of stoichiometry, which is the study of the quantitative relationships between the amounts of reactants used and products formed by a chemical reaction.

For instance, to find out how much of one substance reacts with another, or what amount of product is formed, you would use stoichiometry. It's a methodical process involving the balanced chemical equation for the reaction, the molar masses of the reactants and products, and, often, Avogadro's number to account for the actual number of particles involved in the reaction.