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Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+ and M3+ in its oxide. Fraction of the metal which exists as M3+ would be
  • a)
    5.08%
  • b)
    7.01%
  • c)
    4.08%
  • d)
    6.05%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Experimentally it was found that a metal oxide has formula M0.98O. Met...
Let the fraction o f metal which exists as M2+ be x. Then the fraction of metal as M2+ = (0.98 - x)
3x + 2( 0.98 - x) = 2
x + 1.96 = 2
x = 0.04
% of M3+ = 0.04/0.98 x 100
= 4.08%
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Most Upvoted Answer
Experimentally it was found that a metal oxide has formula M0.98O. Met...
Given: Metal oxide has formula M0.98O. Metal M, is present as M2 and M3 in its oxide.
To find: Fraction of the metal which exists as M3.

Solution:
Let the atomic weight of M be x.
M2+ ion will have (x-2) electrons and M3+ ion will have (x-3) electrons.
Let the fraction of M3+ ion be y.
Then the fraction of M2+ ion will be (1-y).
According to the given formula of metal oxide, the metal is present in the oxide in the ratio of 0.98:1.
Therefore, the mass of metal present in the oxide = 0.98x
From this, we can write the following equation:
(2*(1-y)*(x-2) + 3*y*(x-3))/x = 0.98
(2x - 4 - 2yx + 6y)/x = 0.98
2 - 2y + 6y/x = 0.98
2y/x = 0.02
y/x = 0.01
y = 0.01x
Therefore, the fraction of the metal which exists as M3 is 0.01 or 1%.
To convert this into percentage, we multiply by 100.
Therefore, the required fraction is 1% or 4.08% (option C).

Hence, option C is the correct answer.

Note: This type of problem can be solved by assuming the fraction of M3+ ion as y and then writing the equation based on the number of electrons in M2+ and M3+ ions. Then, solving the equation to find the value of y.
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Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+and M3+ in its oxide. Fraction of the metal which exists as M3+ would bea)5.08%b)7.01%c)4.08%d)6.05%Correct answer is option 'C'. Can you explain this answer?
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