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Liquid A has a density of 1.42g/cm^3 7cm^3 of liquid A is mixed with 125cm^3 of liquid B to make liquid C. Liquid C has a density of 1.05g/cm^3 Find the density of liquid B. Give your answer correct to 2 decimal places.

Question

Liquid A has a density of 1.42g/cm^3
7cm^3 of liquid A is mixed with 125cm^3 of liquid B to make liquid C.
Liquid C has a density of 1.05g/cm^3
Find the density of liquid B.
Give your answer correct to 2 decimal places.

Liquid A has a density of 1.42g/cm^3 7cm^3 of liquid A is mixed with 125cm^3 of liquid B to make liquid C. Liquid C has a density of 1.05g/cm^3 Find the density of liquid B. Give your answer correct to 2 decimal places.

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PhoebeVeteran · Tutor for 12 years

Answer

The density of liquid B is \(1.03g/cm^{3}\), correct to 2 decimal places.

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## Step1: <br />First, we want to find the total mass and volume of mixture liquid C. <br /><br />## Step2: <br />Since we know its density is \(1.05g/cm^3\) and density equals to mass divided by volume, from the total volume (\(7 cm^{3}\) of liquid A added to \(125 cm^{3}\) of liquid B), we calculate that the total mass of liquid C would be mass \(= density × volume\).<br /><br />## Step3: <br />Now, we can find the mass of liquid A because we know its density ( \(1.42 g/cm^{3}\) ) and its volume (\(7 cm^{3}\)). It would be same as calculating the mass of liquid A from: mass \(= density × volume \).<br /><br />## Step4: <br />Therefore to find the mass of liquid B, subtract the mass of liquid A from the total mass of liquid C.<br /><br />## Step5: <br />Indeed, once we have the mass of liquid B, we can find the density of liquid B by dividing its mass by its volume.<br /><br />### Step1 formula: \(Density = \frac{Mass}{Volume} \)<br />### Step2 formula: \(Total mass of C = Density_C × total volume of C \)<br />### Step3 formula: \(Mass_A = Density_A × Volume_A \)<br />### Step4 formula: \(Mass_B = Total mass of C - Mass_A \)<br />### Step5 formula: \(Density_B = \frac{Mass_B}{Volume_B} \)<br /><br /># Calculation Part:<br />## Step1 calculation:<br />No calculation required at this point. <br /><br />## Step2 calculation:<br />Total volume of liquid C = volume of liquid A + volume of liquid B = \(7 cm^{3} + 125 cm^{3} = 132 cm^{3}\)<br />Total mass of liquid C = \(1.05g/cm^{3} × 132cm^{3} = 138.6g\)<br /><br />## Step3 calculation:<br />Mass of liquid A = \(1.42 g/cm^{3} ×7cm^{3} = 9.94 g\)<br /><br />## Step4 calculation:<br />Mass of liquid B = \(138.6g - 9.94g = 128.66g\)<br /><br />## Step5 calculation:<br />Density of liquid B = \(128.66g ÷125 cm^{3} = 1.03 g/cm^{3}\)
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