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Question: The mass to charge ratio \(\left( {\dfrac{M}{e}} \right)\)for a cation is \(1.5 \times {10^{ - 8}}Kg...

The mass to charge ratio (Me)\left( {\dfrac{M}{e}} \right)for a cation is 1.5×10−8KgC−11.5 \times {10^{ - 8}}Kg{C^{ - 1}}. What is the mass (in gm) of this cation?

Explanation

Solution

In this question we can use the mass to charge ratio concept if we know that the mass to charge ratio of a cation is equal to the mass of cation divided by its charge. The mass to charge ratio of a cation is usually equal to the mass of the cation (if the charge is +1 + 1).

Complete answer:
We are given with the mass to charge ratio of cation mass(M)charg⁡e(C)=1.5×10−8KgC−1\dfrac{{mass(M)}}{{ch\arg e(C)}} = 1.5 \times {10^{ - 8}}Kg{C^{ - 1}}
As we know the charge of electron or proton is 1.6×10−19C1.6 \times {10^{ - 19}}C
Therefore, M1.6×10−19C=1.5×10−8KgC−1\dfrac{M}{{1.6 \times {{10}^{ - 19}}C}} = 1.5 \times {10^{ - 8}}Kg{C^{ - 1}}
We can calculate the mass by the above equation, i.e.
M=1.5×10−8×1.6×10−19KgM = 1.5 \times {10^{ - 8}} \times 1.6 \times {10^{ - 19}}Kg
M=2.4×10−27KgM = 2.4 \times {10^{ - 27}}Kg
Now, we need to change the mass into grams
M=2.4×10−27×1000gM = 2.4 \times {10^{ - 27}} \times 1000g
M=2.4×10−24gM = 2.4 \times {10^{ - 24}}g
Therefore the mass of the cation in grams is 2.4×10−24g2.4 \times {10^{ - 24}}g.

Note:
It is important to change the mass of the cation from kilogram to gram as it is given in the question, if it is not mentioned then we can leave the mass in kilogram itself as it is the S.I unit of mass. Also, for the future question we can keep in our mind that the mass of the molecular ion is equal to the molecular weight of the compound. Thus, the mass to charge ratio of the molecular ion is equal to the molecular weight of the compound.