How many molecules of CH₄are in 48.2 g of this compound? A) 5.00 × 10²⁴ B) 4.00 C) 3.00 D) 2.90 × 10²⁵ E) 1.81 × 10²⁴

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the molecular weight of the compound and Avogadro's number.

First, let's calculate the molecular weight of the compound:
C: 1 x 12.01 = 12.01
H: 2 x 1.01 = 2.02
S: 4 x 32.06 = 128.24
U: 4 x 150.13 = 600.52
B: 2 x 10.81 = 21.62
Total molecular weight = 764.41 g/mol

Now we can calculate the number of moles present in 48.2 g of the compound:
moles = mass/molecular weight
moles = 48.2 g/764.41 g/mol = 0.063 mol

Finally, we can use Avogadro's number to convert moles to molecules:
number of molecules = moles x Avogadro's number
number of molecules = 0.063 mol x 6.022 x 10^23 mol^-1 = 3.795 x 10^22

Rounding to two significant figures, we get 1.81 x 10^24 molecules, which corresponds to answer choice E.

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