Question

How mant grams are there in 7.15 x 10^24 molecules of water?

A)11.88g
B)214.02g
C)0.66g
D) 1.29 x 10^26g
E)3.97 x 10^23 g

Answer 1

B. 214.02

Step-by-step explanation:

1 mol of water weighs 18.015 gm and contains 6.023 × 10²³ molecules

From question, We have 7.15 × 10²⁴ molecules

Dividing we get (7.15 × 10 ²⁴) ÷ ( 6.023 × 10²³) = 11.871 molecules

Now, Weight of water = 11.871 × 18.015 = 213.85 which is nearer to option B

Answer 2

`\boxed {\boxed {\sf B. \ 214 \ g }}`

Step-by-step explanation:

We are asked to find the mass of a given number of water (H₂O) molecules.

1. Convert Molecules to Moles

First, we convert molecules to moles. We will use Avogadro's Number or 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance. In this case, the particles are molecules of water. Therefore, there are 6.022 ×10²³ molecules of water in 1 mole of water.

We will convert using dimensional analysis, so we must set up a ratio using the underlined information.

`\frac {6.022 * 10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

We are converting 7.15 × 10²⁴ molecules of water to moles, so we multiply the ratio by that value.

`7.15 * 10^(24) \ molecules \ H_2O*\frac {6.022 * 10^(23) \ molecules \ H_2O}{1 \ mol \ H_2O}`

Flip the ratio so the units of molecules of water cancel each other out.

`7.15 * 10^(24) \ molecules \ H_2O*\frac {1 \ mol \ H_2O} {6.022 * 10^(23) \ molecules \ H_2O}`

`7.15 * 10^(24) *\frac {1 \ mol \ H_2O} {6.022 * 10^(23) }`

`\frac {7.15 * 10^(24)} {6.022 * 10^(23) } \ mol \ H_2O`

`11.87313185\ mol \ H_2O`

2. Convert Moles to Grams

Next, we convert moles to grams. We will use the molar mass. This is the mass of 1 mole of a substance. These values are found on the Periodic Table. They are equivalent to the atomic masses, but the units are grams per mole instead of atomic mass units.

Look up the molar masses of the individual elements in water: hydrogen and oxygen.

• H: 1.008 g/mol
• O: 15.999 g/mol

There is a subscript of 2 after H, so there 2 moles of hydrogen in 1 mole of water. Multiply the molar mass by 2 before adding oxygen's molar mass.

• H₂: 1.008 * 2 = 2.016 g/mol
• H₂O: 2.016 + 15.999 = 18.015 g/mol

We convert using dimensional analysis again and set up another ratio.

`\frac {18.015 \ g \ H_2O}{ 1 \ mol \ H_2O}`

Multiply by the number of moles we just calculated.

`11.87313185 \ mol \ H_2O *\frac {18.015 \ g \ H_2O}{ 1 \ mol \ H_2O}`

The units of moles of water cancel.

`11.87313185 *\frac {18.015 \ g \ H_2O}{ 1 }`

`213.8944703 \ g \ H_2O`

The original measurement of molecules has 3 significant figures, so our answer must have the same. For the number we found, that is the one place. The 8 in the tenths place tells us to round the 3 up to a 4.

`214 \ g \ H_2O`

There are approximately 214 grams of water and choice B is correct.