Question

$3.42\mathrm{g}$ of sucrose is dissolved in $18\mathrm{g}$ water in a beaker. The number of oxygen atoms in the solution is-

• A. $6.68\times {10}^{23}$
• B. $6.09\times {10}^{22}$
• C. $6.022\times {10}^{23}$
• D. $6.68\times {10}^{21}$

Answer 1

The correct option is A

$6.68\times {10}^{23}$

The correct option is (A).

Explanation of the correct option:

Given data:

Given the mass of Sucrose = $3.42\mathrm{g}$

Given the mass of water= $18\mathrm{g}$

The molecular formula of sucrose = ${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$

Avogadro number= ${\mathrm{N}}_{\mathrm{A}}=6.022\times {10}^{23}$

Step 1: Calculation for the molar mass of sucrose(${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$)

The molar mass of sucrose(${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$) =$12\times \mathrm{Aomic}\mathrm{mass}\mathrm{of}\mathrm{carbon}\left(12\right)+22\times \mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{Hydrogen}\left(1\right)+11\times \mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{oxygen}\left(16\right)$

= $12\times 12+22\times 1+11\times 16$

= $144+22+176$= $342\mathrm{g}/\mathrm{mol}$

Step 2: Calculation for the total number of oxygen atoms in Sucrose.

1. Moles of sucrose= $\mathrm{given}\mathrm{mass}÷\mathrm{molar}\mathrm{mass}$ = $3.42÷342=0.01\mathrm{moles}$
2. Number of oxygen atoms in 1 sucrose molecule= $11$

$1\mathrm{mole}$ of sucrose(${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$) contains= $11\times$${\mathrm{N}}_{\mathrm{A}}$ atoms of oxygen

$0.01\mathrm{moles}$ of sucrose(${\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}$) contains= $11\times$$0.01$${\mathrm{N}}_{\mathrm{A}}$ atoms of oxygen

= $0.11$${\mathrm{N}}_{\mathrm{A}}$atoms of oxygen

Step 3: Calculation of the total number of oxygen atoms in water.

1. Moles of water = $\mathrm{given}\mathrm{mass}÷\mathrm{molar}\mathrm{mass}$ = $18÷18=1\mathrm{mole}$
2. Number of oxygen atoms in 1 water molecule= $1$

$1\mathrm{mole}$ of water contains= $1\times$${\mathrm{N}}_{\mathrm{A}}$ atoms of oxygen

$1\mathrm{moles}$ of water contains= $1\times$$1$${\mathrm{N}}_{\mathrm{A}}$ atoms of oxygen

= $1$${\mathrm{N}}_{\mathrm{A}}$ atoms of oxygen

Step 4: Calculation of the total number of oxygen atoms in the solution.

Total number of oxygen atoms= $0.11$$+$$1$= $1.11$${\mathrm{N}}_{\mathrm{A}}$

Number of oxygen atoms in solution= $1.11$$\times 6.022\times {10}^{23}$

=$6.68\times {10}^{23}$

Hence $3.42\mathrm{g}$sucrose is dissolved in $18\mathrm{g}$ water in a beaker. The number of oxygen atoms in the solution is $6.68\times {10}^{23}$.