Step-by-step explanation:
To determine the density of the mixture, first, let's calculate the total mass and total volume of the mixture when three liters of water (density = 1 g/cm³) are mixed with five liters of alcohol (density = 0.8 g/cm³).
Given:
Volume of water = 3 liters = 3000 cm³ (since 1 liter = 1000 cm³)
Volume of alcohol = 5 liters = 5000 cm³
Density of water = 1 g/cm³
Density of alcohol = 0.8 g/cm³
Total volume of the mixture = Volume of water + Volume of alcohol
Total volume = 3000 cm³ + 5000 cm³ = 8000 cm³
Next, let's find the total mass of the mixture:
Mass of water = Volume × Density = 3000 cm³ × 1 g/cm³ = 3000 g
Mass of alcohol = Volume × Density = 5000 cm³ × 0.8 g/cm³ = 4000 g
Total mass of the mixture = Mass of water + Mass of alcohol
Total mass = 3000 g + 4000 g = 7000 g
Finally, let's calculate the density of the mixture:
Density = Total mass / Total volume
Density = 7000 g / 8000 cm³
To convert grams to kilograms and cubic centimeters to cubic meters:
Density = 7000 g / 8000 cm³ * (1 kg / 1000 g) / (1 m³ / 1,000,000 cm³)
Density = 0.875 kg/m³
Therefore, the density of the mixture is 0.875 kg/m³.
