Mixtures and Alligation Questions

Multiple choice
  1. $\displaystyle\frac{7}{3}$
  2. $\displaystyle\frac{5}{4}$
  3. $\displaystyle\frac{19}{13}$
  4. $\displaystyle\frac{15}{19}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a mixture, the adiabatic index gamma_mix = (n1*Cv1 + n2*Cv2) / (n1*Cp1 + n2*Cp2) is not the standard formula. Use Cv_mix = (n1*Cv1 + n2*Cv2) / (n1+n2) and Cp_mix = (n1*Cp1 + n2*Cp2) / (n1+n2). For diatomic, Cv=5R/2, Cp=7R/2. For monatomic, Cv=3R/2, Cp=5R/2. Cv_mix = (2*2.5R + 1*1.5R)/3 = 6.5R/3. Cp_mix = (2*3.5R + 1*2.5R)/3 = 9.5R/3. Ratio = 9.5/6.5 = 19/13.

Multiple choice
  1. $X_m=X_p=X_v$
  2. $X_p=\frac {1}{X_v}$
  3. $X_m=\dfrac {1}{X_P}=\dfrac {1}{X_V}$
  4. $X_V=\dfrac {1}{X_p}=\dfrac {1}{X_m}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For an ideal gas mixture, the mole fraction of a component is equal to its volume fraction and its pressure fraction (Dalton's Law of Partial Pressures). Therefore, Xm = Xp = Xv.

Multiple choice
  1. $3.3$ atm
  2. $3.1$ atm
  3. $0.43$ atm
  4. $\cfrac{1.1}{3}$ atm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total pressure = P_water_vapour + P_oxygen. Aqueous tension (P_water_vapour) is constant at 0.1 atm. P_oxygen = 1.1 - 0.1 = 1.0 atm. If volume is 1/3, P_oxygen becomes 1.0 * 3 = 3.0 atm. Total pressure = 3.0 + 0.1 = 3.1 atm.

Multiple choice
  1. $34.5$
  2. $25.0$
  3. $23.0$
  4. $20.0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The reaction is N2O4 -> 2NO2. If NO2 is 50% of the volume, the mole fraction of NO2 is 0.5 and N2O4 is 0.5. The average molar mass is (0.5 * 46) + (0.5 * 92) = 23 + 46 = 69. Vapour density is molar mass / 2, which is 69 / 2 = 34.5.

Multiple choice
  1. $2$  litres and  $14$  litres
  2. $8$  litres and $35$  litres
  3. $7$  litres and $25$  litres
  4. $6$  litres and $15$  litres
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x litres of 90% and (21 - x) litres of 97% be mixed. Then 0.90x + 0.97(21 - x) = 0.95*21, giving x = 6 litres of 90% solution and 15 litres of 97% solution.

Multiple choice
  1. $1.5$
  2. $2.5$
  3. $2$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using Boyle's Law (P1V1 = P2V2) for each gas in the new volume (1L): Oxygen: 1 atm * 1 L = P_O2 * 1 L => P_O2 = 1 atm. Nitrogen: 0.5 atm * 2 L = P_N2 * 1 L => P_N2 = 1 atm. Total pressure = 1 + 1 = 2 atm.

Multiple choice
  1. $1:3$
  2. $2:3$
  3. $3:2$
  4. $5:3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Glass 1: 1/2 milk, 1/2 water. Glass 2: 3/4 milk, 1/4 water. Total milk = 1/2 + 3/4 = 5/4. Total water = 1/2 + 1/4 = 3/4. Ratio of milk to water = (5/4) / (3/4) = 5/3.

Multiple choice
  1. $53$ kgs
  2. $80$ kgs
  3. $36$ kgs
  4. $44$ kgs
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Alloy X (60 kg) has lead and tin in ratio 3:2, so tin = (2/5)*60 = 24 kg. Alloy Y (100 kg) has tin and copper in ratio 1:4, so tin = (1/5)*100 = 20 kg. Total tin = 24 + 20 = 44 kg.