Respuesta :
Answer:
Mass of liquid B = 271.2 gram
Explanation:
Given:
Density of liquid A = 1000 kg/m³
Density of liquid B = 600 kg/m³
Density of mixture = 850 kg/m³
Mass of mixture = 1 kg
Assume:
Volume of liquid A = Va
Volume of liquid B = Vb
So,
Volume of mixture = Va + Vb
Mass of liquid A = 1000(Va)
Mass of liquid B = 600(Vb)
Mass of mixture = Mass of liquid A + Mass of liquid B
1 = 1000(Va) + 600(Vb)
Volume of mixture = 1 / 850
So,
(1/850) = Va + Vb
Vb = (1/850) - Va
1 = 1000(Va) + 600[(1/850) - Va]
Va = 7.25 × 10⁻⁴
Vb = (1/850) - Va
Vb = (1/850) - [7.25 × 10⁻⁴]
Vb = 4.25 × 10⁻⁴
Mass of liquid B = 600(Vb)
Mass of liquid B = 600(4.25 × 10⁻⁴)
Mass of liquid B = 271.2 gram
The mass of liquid B in the 1 Kg mixture is 300 g
Let the volume of liquid A be Va
Let the volume of liquid B be Vb
From the question given above, the following data were obtained:
Density of liquid A = 1000 kg/m³
Density of liquid B = 600 kg/m³
Density of mixture = 850 kg/m³
Mass of mixture = 1 kg
Mass of Liquid B (in grams) =?
- Next, we shall determine the mass of liquid A and B
For Liquid A:
Density of liquid A = 1000 kg/m³
Volume of liquid A = Va
Mass of Liquid A =?
Mass = Density × Volume
Mass of Liquid A = 1000 × Va
Mass of liquid A = 1000(Va)
For Liquid B:
Density of liquid B = 600 kg/m³
Volume of liquid B= Va
Mass of Liquid B =?
Mass = Density × Volume
Mass of Liquid B = 600 × Va
Mass of liquid B = 600(Vb)
- Next, we shall determine the volume of the mixture.
Density of mixture = 850 kg/m³
Mass of mixture = 1 kg
Volume of mixture =?
Volume = mass /density
Volume of mixture = 1 / 850
Volume of mixture = 0.0012 m³
- Next, we shall determine the volume of liquid A
Mass of mixture = 1 Kg
Mass of mixture = Mass of liquid A + Mass of liquid B
1 = 1000(Va) + 600(Vb) ....... (1)
Volume of mixture = Va + Vb
Volume of mixture = 0.0012 m³
Thus,
0.0012 = Va + Vb
Vb = 0.0012 – Va ........ (2)
Substitute Vb in equation 2 into equation (1)
1 = 1000(Va) + 600[0.0012 – Va]
1 = 1000Va + 0.72 – 600Va
Collect like terms
1 – 0.72 = 1000Va – 600Va
0.28 = 400Va
Divide both side by 400
Va = 0.28 / 400
Va = 0.0007 m³
- Next, we shall determine the volume of the liquid B
Volume of mixture = 0.0012 m³
Volume of liquid A (Va) = 0.0007 m³
Volume of liquid B (Vb) =?
Vb = 0.0012 – Va
Vb = 0.0012 – 0.0007
Vb = 0.0005 m³
- Finally, we shall determine the mass of liquid B
Volume of liquid B (Vb) = 0.0005 m³
Mass of liquid B = 600(Vb)
Mass of liquid B = 600(0.0005)
Mass of liquid B = 0.3 Kg
Multiply by 1000 to express in grams
Mass of liquid B = 0.3 × 1000
Mass of liquid B = 300 g
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