Question

Calculate the molar mass of a compound if \(0.372 \mathrm{~mol}\) of it has a mass of \(152 \mathrm{~g}\).

Short answer

The molar mass of the compound is approximately 408.60 g/mol.

Step-by-step solution

Understand the Relationship

The molar mass (M) of a compound represents the mass of one mole of that compound. It can be calculated using the formula: \[ M = \frac{\text{Mass of sample (in grams)}}{\text{Amount of substance (in moles)}} \]

Determine Known Values

From the given data, we have:- Mass of the sample: \(152 \text{ g}\)- Amount of substance: \(0.372 \text{ mol}\)

Apply the Formula

Substitute the known values into the formula: \[ M = \frac{152 \text{ g}}{0.372 \text{ mol}} \]

Calculate the Molar Mass

Perform the division:\[ M = \frac{152}{0.372} \approx 408.60 \text{ g/mol} \]

Verify the Units

Ensure that the resulting units are in grams per mole (g/mol), which they are, confirming the correct calculation of the molar mass.

Key concepts

Mass of Sample

The "mass of the sample" refers to the amount of matter that you're dealing with in terms of weight. When we talk about mass in chemistry, it's important to know that it's typically measured in grams. This is because grams are a part of the metric system, which is universally used in scientific work. Understanding the mass of a sample is crucial since it enables chemists to determine the amount of any given compound within a mixture. This, in turn, helps in calculating other important chemical properties, like the molar mass. Here's how you can think about it:

• If you have a sample of a compound, and you know it weighs 152 grams, this is the sample's mass.
• To find the molar mass of this compound, you would use this mass in your calculations.

Moreover, knowing the mass can help you ensure that you're using the correct amount of a compound for chemical reactions or experiments. In our example, the conversion from sample mass to molar mass is straightforward because we already have the mass measured in grams, making the calculation process simpler.

Amount of Substance

The "amount of substance" is a fundamental concept in chemistry, representing the number of entities, like atoms or molecules, present in a sample. This is typically measured in moles—and here's why it matters: The mole (abbreviated as mol) is a standard scientific unit for measuring large quantities of very tiny entities, such as atoms, molecules, or other specified particles. The concept is based on Avogadro's number, which is approximately 6.022 x 10²³, representing the number of atoms in 12 grams of pure carbon-12. In our exercise, the amount of substance is given as 0.372 moles. This means you have 0.372 times the number of particles contained in Avogadro's number.

• Knowing the moles helps in comparing quantities of different substances.
• This is especially useful when dealing with chemical reactions, where reactants and products are often measured in moles.

Understanding the amount of substance helps in determining the stoichiometry in reactions, which is crucial for balancing chemical equations and for making efficient use of chemicals in lab experiments.

Grams per Mole

The term "grams per mole" refers to molar mass, a critical concept in chemistry that provides a direct way to convert between the mass of a substance and the amount of its constituent particles. Molar mass is expressed in grams per mole (g/mol), allowing one to easily relate the mass of a chemical sample to the number of moles it contains.In the given exercise, the molar mass is calculated using the relationship:\[ M = \frac{\text{Mass of sample (in grams)}}{\text{Amount of substance (in moles)}} \]This relationship helps in finding out how much one mole of a compound weighs. For instance:

• If a compound's sample mass is 152 grams and it contains 0.372 moles, its molar mass is found by: \[ M = \frac{152}{0.372} \approx 408.60 \text{ g/mol} \]
• This indicates that one mole of this compound weighs approximately 408.60 grams.

With this information, chemists can accurately prepare solutions and reactants for experiments based on precise mass measurements, knowing the exact amount of substance needed for each reaction.