What is the mass of $2.01 \times 10^{23}$ formula units of $CoSO_4$?
($1 mol CoSO_4 = 154.99 g$)
($1 mol CoSO_4 = 6.02 \times 10^{23}$ formula units)
[?] g $CoSO_4$
Answer (2)
Convert the number of formula units to moles using Avogadro's number: m o l es = 6.02 × 1 0 23 2.01 × 1 0 23 = 0.333886 .
Convert moles to grams using the molar mass of C o S O 4 : ma ss = 0.333886 mol × 154.99 g/mol .
Calculate the mass: ma ss = 51.749 g .
The mass of 2.01 × 1 0 23 formula units of C o S O 4 is 51.75 g .
Explanation
Problem Analysis We are given the number of formula units of C o S O 4 and asked to find its mass in grams. We are also given the molar mass of C o S O 4 and Avogadro's number, which relates the number of formula units to moles.
Converting Formula Units to Moles First, we need to convert the number of formula units to moles. We know that 1 mole of C o S O 4 contains 6.02 × 1 0 23 formula units. Therefore, we can calculate the number of moles of C o S O 4 as follows: m o l es = Avogadro’s number number of formula units = 6.02 × 1 0 23 2.01 × 1 0 23
Calculating Moles Now, we calculate the number of moles: m o l es = 6.02 × 1 0 23 2.01 × 1 0 23 = 0.333886 mol
Converting Moles to Grams Next, we need to convert the number of moles to grams. We know that 1 mole of C o S O 4 has a mass of 154.99 g. Therefore, we can calculate the mass of C o S O 4 as follows: ma ss = m o l es × molar mass = 0.333886 mol × 154.99 g/mol
Calculating Mass Now, we calculate the mass: ma ss = 0.333886 × 154.99 = 51.749 g Therefore, the mass of 2.01 × 1 0 23 formula units of C o S O 4 is approximately 51.75 g.
Final Answer The mass of 2.01 × 1 0 23 formula units of C o S O 4 is approximately 51.75 g.
Examples
Imagine you are a chemist and need to measure out a specific amount of a chemical compound, Cobalt Sulfate ( C o S O 4 ), for an experiment. Knowing the relationship between the number of formula units, moles, and mass allows you to accurately convert between these units. For instance, if you need 2.01 × 1 0 23 formula units of C o S O 4 , you can calculate the mass needed, which is approximately 51.75 g. This ensures you have the correct amount of the compound for your experiment, leading to accurate and reliable results. This conversion is a fundamental skill in chemistry, crucial for preparing solutions and conducting experiments.
The mass of 2.01 × 1 0 23 formula units of C o S O 4 is approximately 51.75 g, calculated by converting formula units to moles using Avogadro's number, and then converting moles to grams using the molar mass. The calculation shows that 0.333886 moles of cobalt sulfate (with a molar mass of 154.99 g/mol) corresponds to this mass.
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