Question

Dimethyl sulfoxide [(ch3)2so], also called dmso, is an important solvent that penetrates the skin, enabling it to be used as a topical drug-delivery agent. calculate the number of c, s, h, and o atoms in 7.14 × 103 g of dimethyl sulfoxide.

Answer 1

The molecular formula of dimethyl sulfoxide is $(CH_{3})_{2}SO$. Molar mass of dimethyl sulfoxide is 78.13 g/mol. Calculate number of moles as follows:

$n=\frac{m}{M}=\frac{7.14\times 10^{3} g}{78.13 g/mol}=91.38 mol$

From the molecular formula, 1 mole of dimethyl sulfoxide contains 2 moles of Carbon, 6 moles of Hydrogen, 1 mole of Sulfur and 1 mole of oxygen.

Thus, 91.38 moles of dimethyl sulfoxide will have:

Carbon :

$n_{C}=2\times 91.38 moles=182.77 moles$

Hydrogen:

$n_{H}=6\times 91.38 moles=548.28 moles$

Sulfur:

$n_{S}=1\times 91.38 moles=91.38 moles$

Oxygen:

$n_{O}=1\times 91.38 moles=91.38 moles$

Since, 1 mole of an element equals to $6.023\times 10^{23}$ atoms thus, number of atoms can be calculated as:

Carbon:

$1 mole\rightarrow 6.023\times 10^{23} atoms$

Thus,

$182.77 moles\rightarrow 182.77\times 6.023\times 10^{23} atoms=1.10\times 10^{26} atoms$

Hydrogen:

$1 mole\rightarrow 6.023\times 10^{23} atoms$

Thus,

$548.28 moles\rightarrow 548.28\times 6.023\times 10^{23} atoms=3.30\times 10^{26} atoms$

Sulfur:

$1 mole\rightarrow 6.023\times 10^{23} atoms$

Thus,

$91.38 moles\rightarrow 91.38\times 6.023\times 10^{23} atoms=5.50\times 10^{25} atoms$

Oxygen:

$1 mole\rightarrow 6.023\times 10^{23} atoms$

Thus,

$91.38 moles\rightarrow 91.38\times 6.023\times 10^{23} atoms=5.50\times 10^{25} atoms$

Therefore, number of C, S, H and O atoms are $1.10\times 10^{26}, 5.50\times 10^{25}, 3.30\times 10^{26} and 5.50\times 10^{25} atoms$ respectively.