Question

A given mixture consists only of pure substance \(\mathrm{X}\) and pure substance \(\mathrm{Y}\). The total mass of the mixture is \(3.72 \mathrm{~g}\). The total number of moles is \(0.06\). If the mass of one mole of \(Y\) is \(48 \mathrm{~g}\) and there is \(0.02\) mole of \(\mathrm{X}\) in the mixture, what is the mass of one mole of \(\mathrm{X}\) ? (a) \(90 \mathrm{~g}\) (b) \(75 \mathrm{~g}\) (c) \(45 \mathrm{~g}\) (d) \(180 \mathrm{~g}\)

Short answer

Answer: The mass of one mole of substance X is 90 g.

Step-by-step solution

Determine the number of moles of substance Y

We know that there are a total of 0.06 moles in the mixture, and there are 0.02 moles of X. To find the number of moles of substance Y, we subtract moles of X from the total moles: 0.06 - 0.02 = 0.04 moles of Y.

Find the mass of substance Y

We know that the mass of one mole of Y is 48 g. To find the mass of 0.04 moles of Y, multiply 0.04 by the mass of one mole of Y: 0.04 * 48 = 1.92 g.

Find the mass of substance X

We know the total mass of the mixture is 3.72 g and the mass of Y is 1.92 g. Subtract the mass of Y from the total mass to find the mass of X: 3.72 - 1.92 = 1.80 g.

Calculate the mass of one mole of substance X

We know that there are 0.02 moles of X in the mixture, and the mass of X is 1.80 g. Divide the mass of X by the number of moles of X to find the mass of one mole of X: 1.80 / 0.02 = 90 g. Since the mass of one mole of X is 90 g, the answer is: (a) \(90 \mathrm{~g}\).

Key concepts

Stoichiometry

Stoichiometry lies at the heart of chemistry, providing a methodological basis for understanding how substances react with one another in fixed proportions. It is rooted in the law of conservation of mass, which states that mass in an isolated system is neither created nor destroyed by chemical reactions.

In the context of our exercise, stoichiometry allows us to discern the relation between masses and moles of substances in a chemical mixture. Using stoichiometric calculations, we can determine the amount of reactants needed to produce a certain amount of product or, as in our case, calculate the molar mass of a compound given the mass and the number of moles present. This fundamental concept enables us to navigate through chemical equations and reactant-product relationships with ease, ensuring that quantitatively, our chemical reactions are balanced and accurate.

Chemical Mixture

A chemical mixture consists of two or more substances that are physically combined. Each substance in the mixture retains its own chemical properties and may exist in any proportion. In our case, the mixture is composed of substances X and Y, and knowing the total mass of the mixture is crucial for subsequent calculations.

When dealing with mixtures, it becomes essential to differentiate between the different components, as each can contribute differently to the overall properties of the mixture. Stoichiometric principles assist in parsing out the individual contributions—such as determining the mass of one substance when the total mass and the mass of the other substance are known, which is at the heart of solving our given problem.

Molar Mass Calculation

Molar mass calculation is a pivotal skill in chemistry that involves determining the mass of one mole of a substance. The mole is a fundamental unit in chemistry, analogous to the 'dozen' in everyday life, and it represents Avogadro's number \(6.022\times10^{23}\) of particles. Molar mass is thus the mass of this gargantuan number of molecules or atoms, typically expressed in grams per mole (g/mol).

To calculate the molar mass, as illustrated in our exercise, one divides the given mass of the substance by the number of moles. This is depicted by the formula: \[ Molar \ Mass = \frac{Mass \ of \ Substance}{Number \ of \ Moles} \] This step is fundamental in identifying unknown substances in a mixture or determining the proportions needed for a reaction. By establishing the molar mass, we gain insight into the amount of substance and how it interacts in various chemical processes.