Question

The cost of table salt (NaCl) and table sugar (C₁₂H₂₂O₁₁) is 2rs per kg and 6rs per kg, respectively. Calculate their costs per mole.

Answer 1

Step-1 Calculating the mass of table salt $\left(\mathrm{NaCl}\right)$and table sugar $\left(C_{12}{H}_{22}{O}_{11}\right)$

(a) The atomic mass of $\mathrm{Na}$ $=23g$

The atomic mass of $\mathrm{Cl}$= $35.5g$

$\mathrm{Molar}\mathrm{mass}\mathrm{of}\mathrm{table}\mathrm{salt}\left(\mathrm{NaCl}\right)=\mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{Na}+\mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{Cl}$

$=23+35.5==58.5g$

(b) The atomic mass of$\mathrm{C}$=$12g$

The atomic mass of $\mathrm{H}$=$1g$

The atomic mass of $\mathrm{O}$=$16g$

$molarmassoftablesugar(C_{12}{H}_{22}{O}_{11})=(11\times AtomicmassofO)+(12\times AtomicmassofC)+2(2\times AtomicmassofH)$

$=(11\times 16)+(12\times 12)+(22\times 1)=342g$

Step-2 Calculating the costs per mole of table salt and sugar

(a) $1000g$ of table salt costs= $2rs$

$1g$ of salt costs= $2rs/1000g$

$58.5g$(1mole) of salt costs =$\left(2rs/1000g\right)\times 58.5g=0.117rs/mole$

(b) $1000g$of table sugar costs= $6rs$

$1g$of salt costs= $6rs/1000g$

$342g$ (1mole) of sugar costs =$\left(6rs/1000g\right)\times 342g=2.052rs/mole$

Hence, Cost of table salt$\left(\mathrm{NaCl}\right)$ = $0.117rs/mole$

Cost of table sugar $\left({\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}\right)$ = $2.052rs/mole$