Three litres of water 1g/cm^3 is added to twelve litres of alcohol density 0.8g/cm^3.What is the density of the mixture?
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
= ....
Math
To find the density of the mixture, we can use the formula:
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.
To find the density of the mixture, we need to consider the total mass and the total volume of the mixture.
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.