The density of ethanol is 1.09 g/cm³
The density of propylene is 0.97 g/cm³
60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3
Question 14
The density of ethanol is 1.09 g/cm³
The density of propylene is 0.97 g/cm³
60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifr... show full transcript
Worked Solution & Example Answer:The density of ethanol is 1.09 g/cm³
The density of propylene is 0.97 g/cm³
60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 3
Step 1
Calculate the Mass of Ethanol
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Answer
First, we convert the volume of ethanol to mass using its density:
Mass of ethanol = Density × Volume = 1.09 g/cm³ × 60 L
We convert 60 L to cm³: 60 L = 60000 cm³, so:
Mass of ethanol = 1.09 g/cm³ × 60000 cm³ = 65400 g.
Step 2
Calculate the Mass of Propylene
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Answer
Next, we use the density of propylene to calculate its mass:
Mass of propylene = Density × Volume = 0.97 g/cm³ × 128 L
Convert 128 L to cm³: 128 L = 128000 cm³, thus:
Mass of propylene = 0.97 g/cm³ × 128000 cm³ = 124096 g.
Step 3
Calculate the Total Mass of Antifreeze
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Answer
Now, we find the total mass of the antifreeze by summing the masses of ethanol and propylene:
Total Mass = Mass of ethanol + Mass of propylene = 65400 g + 124096 g = 189496 g.
Step 4
Calculate the Density of Antifreeze
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Answer
Finally, we calculate the density of the antifreeze using the total mass and total volume:
Density = Total Mass / Total Volume
The total volume of antifreeze is 188 L, which is 188000 cm³:
Density = 189496 g / 188000 cm³ ≈ 1.008 g/cm³.
Rounding to two decimal places, the density of the antifreeze is approximately 1.01 g/cm³.
