How many grams would [tex]$3.36 \times 10^{23}$[/tex] molecules of copper (II) sulfate ([tex]$CuSO_4$[/tex]) weigh?
A. [tex]$5.55 g$[/tex]
B. 89.03 g
C. 8.903 g
D. 0.5578 g
Answer (2)
Calculate the molar mass of C u S O 4 : M ( C u S O 4 ) = 63.546 + 32.06 + 4 × 16.00 = 159.606 g/mol.
Convert the number of molecules to moles: m o l es = 6.022 × 1 0 23 3.36 × 1 0 23 = 0.55795 mol.
Calculate the mass in grams: ma ss = 0.55795 × 159.606 = 89.0528 g.
The mass of 3.36 × 1 0 23 molecules of C u S O 4 is approximately 89.03 g .
Explanation
Problem Analysis We are given $3.36
\times 10^{23} m o l ec u l eso f co pp er ( II ) s u l f a t e ( CuSO_4 ) an d a s k e d t o f in d i t s ma ss in g r am s . T o d o t hi s , w e w i ll f i rs t c a l c u l a t e t h e m o l a r ma sso f CuSO_4$, then convert the number of molecules to moles, and finally convert moles to grams.
Calculating Molar Mass of CuSO4 First, we need to find the molar mass of C u S O 4 . The molar mass is the sum of the atomic masses of each element in the compound. We have:
Copper (Cu): 63.546 g/mol
Sulfur (S): 32.06 g/mol
Oxygen (O): 16.00 g/mol
So, the molar mass of C u S O 4 is:
$M(CuSO_4) = M(Cu) + M(S) + 4
\times M(O) = 63.546 + 32.06 + 4
\times 16.00 = 63.546 + 32.06 + 64.00 = 159.606$ g/mol
Converting Molecules to Moles Next, we need to convert the number of molecules to moles. We use Avogadro's number, $N_A = 6.022
\times 10^{23}$ molecules/mol. The number of moles is given by:
$moles =
\frac{number
of
molecules}{N_A} =
\frac{3.36
\times 10^{23}}{6.022
\times 10^{23}} = 0.55795$ mol
Calculating Mass in Grams Now, we can calculate the mass in grams using the formula:
$mass = moles
\times molar
mass = 0.55795
\times 159.606 = 89.0528$ g
Rounding to two decimal places, we get 89.05 g. The closest answer is 89.03 g.
Final Answer Therefore, $3.36
\times 10^{23} m o l ec u l eso f co pp er ( II ) s u l f a t e ( CuSO_4$) weigh approximately 89.05 grams.
Examples
Imagine you're a chemist and need to measure out a specific amount of a chemical compound for an experiment. Knowing how to convert between the number of molecules and mass is crucial. For instance, if you need exactly 3.36 × 1 0 23 molecules of copper (II) sulfate for a reaction, you would calculate the mass needed, which is approximately 89.05 grams. This ensures you have the correct amount of the substance for your experiment to work as expected. This calculation is also important in pharmaceutical industry, where precise quantities of compounds are needed to formulate drugs.
The weight of 3.36 × 1 0 23 molecules of copper (II) sulfate ( C u S O 4 ) is approximately 89.05 grams. The calculated molar mass of C u S O 4 is 159.606 g/mol, and using Avogadro's number, we find it corresponds to around 0.55795 moles. Thus, the best answer choice is B. 89.03 g.
;
