Mixtures and Alligation Questions

Multiple choice
  1. $80^o$C
  2. $60^o$C
  3. $70^o$C
  4. $85^o$C
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the heat balance equation m1*c1*(T1-T) = m2*c2*(T-T2). First case: 100*c1*(100-90) = 50*c2*(90-75) => 1000*c1 = 750*c2 => c1/c2 = 0.75. Second case: 100*0.75*(100-T) = 50*(T-50) => 7500 - 75T = 50T - 2500 => 125T = 10000 => T = 80.

Multiple choice
  1. $\displaystyle { 29 }^{ \circ }C$
  2. $\displaystyle { 25 }^{ \circ }C$
  3. $\displaystyle { 20 }^{ \circ }C$
  4. $\displaystyle { 16 }^{ \circ }C$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice
  1. $5\times 10^{4}$
  2. $5\times 10^{-3}$
  3. $5\times 10^{-2}$
  4. $5\times 10^{-1}$
  5. $5$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Concentration in ppm is defined as (mass of solute / mass of solution) * 10^6. Here, mass of solute = 5 * 10^-3 g and mass of solution = 1 kg = 1000 g. Thus, (5 * 10^-3 / 1000) * 10^6 = 5 * 10^-3 * 10^3 = 5 ppm.

Multiple choice
  1. $\sqrt{\rho_A \rho_B}$
  2. $\frac{\rho_A + \rho_B}{2}$
  3. $\frac{\rho_A \rho_B}{\rho_A + \rho_B}$
  4. $\frac{2\rho_A \rho_B}{\rho_A + \rho_B}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The density of a mixture is the total mass divided by the total volume. With equal masses m, the total mass is 2m and the total volume is m/rho_A + m/rho_B, which simplifies to 2*rho_A*rho_B / (rho_A + rho_B).

Multiple choice
  1. $2.0$
  2. $3.0$
  3. $3.5$
  4. $4.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let densities be d1, d2. Equal volume: (d1+d2)/2 = 4 => d1+d2 = 8. Equal weight: 2/(1/d1 + 1/d2) = 3 => 2d1d2/(d1+d2) = 3. 2d1d2/8 = 3 => d1d2 = 12. Roots of x^2 - 8x + 12 = 0 are 6 and 2. Ratio is 6/2 = 3.