Question

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

Short answer

A mass of $0.505\mathrm{g}$ of hydrogen contains the same number of atoms as $7.00\mathrm{g}$ of nitrogen.

Step-by-step solution

Calculate the number of moles of nitrogen

To find the number of moles of nitrogen in 7.00 g, we can use the formula: Number of moles = mass / molar mass The molar mass of nitrogen (N₂) is 28.02 g/mol. So, the number of moles of nitrogen in 7.00 g is: Number of moles of N₂ = 7.00 g / 28.02 g/mol = 0.250 moles

Find the number of atoms of nitrogen

Since nitrogen is in the form of N₂, we need to find the number of N atoms. As one mole of N₂ contains two moles of nitrogen atoms, we can calculate the number of moles of nitrogen atoms by: Number of moles of N atoms = 2 * moles of N₂ = 2 * 0.250 moles = 0.500 moles

Calculate the mass of hydrogen

We now know that there are 0.500 moles of nitrogen atoms. We can assume that the number of atoms in hydrogen is equal to the number of atoms in nitrogen. Since hydrogen is in the form of H₂, we need to find the number of moles of H₂ before finding their mass: Number of moles of H₂ = 0.500 moles of N atoms / 2 = 0.250 moles The molar mass of hydrogen (H₂) is 2.02 g/mol. To find the mass of hydrogen, we can now use the formula: Mass of hydrogen = moles of hydrogen * molar mass of hydrogen Mass of hydrogen = 0.250 moles * 2.02 g/mol = 0.505 g Hence, a mass of 0.505 g of hydrogen contains the same number of atoms as 7.00 g of nitrogen.

Key concepts

Molar Mass

Molar mass is a foundational concept in chemistry that refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essentially the weight of Avogadro's number of particles (atoms, molecules, or ions) of a substance. The molar mass is calculated by summing the atomic masses of all the atoms in a molecule.

For example, in our exercise, the molar mass of nitrogen (N₂) is 28.02 g/mol. This number is fundamental for converting mass to moles, which is crucial in understanding the quantities involved in chemical reactions and enables chemists to count atoms by weighing, facilitating the stoichiometry calculations seen in the exercise.

Relating Molar Mass to Stoichiometry

Recognizing the direct proportionality between mass and moles provided by the molar mass, it becomes a pivotal part of stoichiometric calculations. Given the mass of a substance, dividing by its molar mass yields the number of moles, which subsequently aligns with Avogadro's number to provide the number of particles, tying our macroscopic measurements to the microscopic world.

Moles to Atoms Conversion

Making the leap from moles to atoms is a critical conversion in chemistry that hinges on Avogadro's number, which is approximately 6.022 x 10²³. This number represents the quantity of particles in one mole of a substance. To convert from moles to atoms (or molecules), one simply multiplies the number of moles by Avogadro's number.

In the step by step solution to our exercise, we initially find the number of moles of nitrogen atoms to be 0.500 moles. Knowing that this represents a vast number of individual atoms, we match it to the same number of hydrogen atoms and convert backwards to find the moles and then mass of hydrogen, ensuring equal numbers of each species, as demanded by stoichiometry.

Practical Insights in Conversion

Understanding this moles to atoms conversion is essential not just in solving textbook problems but in practical applications like determining amounts of reactants for reactions and analyzing substance composition. The conversion also solidifies the concept of the mole as a bridge between the atomic scale and the real-world scale.

Chemical Composition

Chemical composition details the identity and proportion of the elements within a compound. Each substance has a unique makeup that determines its physical and chemical properties. In context, understanding the chemical composition of a compound allows us to manipulate and quantify it during chemical reactions.

For instance, in our textbook exercise, nitrogen exists as a diatomic molecule (N₂), and hydrogen also exists diatomically as (H₂). This knowledge of chemical composition is essential for stoichiometric calculations because it affects the mole ratio used in converting between substances.

Impact on Stoichiometric Calculations

Chemical composition is central to stoichiometry because it dictates the mole ratios in balanced chemical equations. Knowing the composition of the reactants and products allows chemists to predict the outcome of reactions and calculate exact amounts needed for a reaction to occur without excess, making it indispensable in fields such as pharmaceuticals, material manufacturing, and environmental science.