Question

The cost of electricity required to deposit $1gm$ of $Mg$ is $Rs.5.$. How much would it cost to deposit $10gm$. of $Al?(Atwt.Al=27,Mg=24)$

• A. $Rs.10.00$
• B. $Rs.27.00$
• C. $Rs.44.44$
• D. $Rs.66.67$

Answer 1

The correct option is C $Rs.44.44$

For Magnesium

$m=1$ gm

$M=24$ gm

$No.ofMoles=\frac{Mass}{Molarmass}$

$No.ofMoles=\frac{1}{24}=0.04$ moles

No. of atoms in $1$ mole $=6.022\times {10}^{23}$

No. of atoms in $0.04$ mole $=0.04\times 6.022\times {10}^{23}=2.4\times {10}^{22}$ atoms

For Aluminium

$m=10$ g

$M=27$ g

$No.ofmoles=\frac{10}{27}=0.37$ moles

No. of atoms in $0.37$ moles$=0.37\times 6.022\times {10}^{23}=2.2\times {10}^{23}$ atoms

According to question

cost to deposit $2.4\times {10}^{22}$ atoms is $=$Rs $5$

Cost to deposit $2.3\times {10}^{23}$ atoms is $=\frac{5}{2.4\times {10}^{22}}\times 2.2\times {10}^{23}=44$ Rs