density = total mass/total volume
3 l of water ----> 3000g
12 l of alcohol ----> 12000(.8) = 9600 g
density = (3000+9600)g/15000 cm^3
= ....
3 l of water ----> 3000g
12 l of alcohol ----> 12000(.8) = 9600 g
density = (3000+9600)g/15000 cm^3
= ....
Density = (mass of substance) / (volume of substance)
First, let's calculate the mass of water added:
Mass of water = Volume of water × Density of water
Given that the volume of water added is 3 liters (which is equal to 3000 cm^3) and the density of water is 1 g/cm^3:
Mass of water = 3000 cm^3 × 1 g/cm^3 = 3000 g
Next, let's calculate the mass of alcohol:
Mass of alcohol = Volume of alcohol × Density of alcohol
Given that the volume of alcohol is 12 liters (which is equal to 12000 cm^3) and the density of alcohol is 0.8 g/cm^3:
Mass of alcohol = 12000 cm^3 × 0.8 g/cm^3 = 9600 g
Now, let's calculate the total mass of the mixture:
Total mass = Mass of water + Mass of alcohol
Total mass = 3000 g + 9600 g = 12600 g
The total volume of the mixture is the sum of the volumes of water and alcohol added:
Total volume = Volume of water + Volume of alcohol = 3000 + 12000 = 15000 cm^3
Finally, let's calculate the density of the mixture using the formula mentioned earlier:
Density of mixture = Total mass / Total volume
Density of mixture = 12600 g / 15000 cm^3 = 0.84 g/cm^3
Therefore, the density of the mixture is 0.84 g/cm^3.
Let's start by finding the mass of water and alcohol separately:
Mass of water = Volume of water × Density of water
= 3 litres × 1 g/cm^3
= 3 g
Mass of alcohol = Volume of alcohol × Density of alcohol
= 12 litres × 0.8 g/cm^3
= 9.6 g
Now, let's find the total mass of the mixture:
Total mass = Mass of water + Mass of alcohol
= 3 g + 9.6 g
= 12.6 g
Next, let's find the total volume of the mixture:
Total volume = Volume of water + Volume of alcohol
= 3 litres + 12 litres
= 15 litres
Finally, we can calculate the density of the mixture:
Density of mixture = Total mass / Total volume
= 12.6 g / 15 litres
To get the density of the mixture in g/cm^3, we need to convert litres to cm^3 since 1 litre is equal to 1000 cm^3:
Density of mixture = 12.6 g / (15 litres × 1000 cm^3/litre)
= 12.6 g / 15000 cm^3
= 0.00084 g/cm^3
Therefore, the density of the mixture is approximately 0.00084 g/cm^3.