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Question

Correct expressions among the following are: (ρ - density of solution; M - molarity of solution, M2 - Molar mass of solute; mmolality;X2 - Mole fraction of solute).

A
m=1000M1000ρMM2
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B
X2=mM11+mM1
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C
X2=MM1M(M1M2)+ρ
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D
m=ρMM2M
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Solution

The correct option is A m=1000M1000ρMM2
X2=n2n1+n2=n2m1/M1+n2=n2M1m1+n2M1=n2M1(m1+m2)+n2M1m2=n2M1Vρ+n2(M1+M2)
=(n2/V)M1ρ+(n2V)(M1+M2)=MM1ρ+M(M1M2)
Also,
m=1000M1000ρM×M2
Let, mass of solute be W2 and solvent be W1
M=W2M2×1000V (Equation 01)
m=WM2×1000W1 (Equation 02)
ρ=W+W2V
V=W2×1000MM2 mL (From 01)
So,
W1+W2=W2+1000W2mM2
W1+W2=1000M2(mM21000m+1m)W1
ρM=1m+M21000
m=M×10001000ρMM2

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