Question

A mixture of alcohol and water has the density 750 kg m 3.calculate the ratio in the mixture of alcohol to water by i.mass ii.volume

Don't know.

According to Google, the density of ethanol ("alcohol") is 789 kg/m³.
So if the liquid has a density of 750 kg/m³, i.e. it is less than the density of ethanol, it must be something else. If ethanol is mixed with water, the density goes up, i.e. ≥ 789 kg/m³.

See also
http://wissen.science-and-fun.de/chemistry/chemistry/density-tables/ethanol-water-mixtures/
for confirmation.

To calculate the ratio of alcohol to water in the mixture, we need to determine the quantities of alcohol and water present in both mass and volume.

Let's assume that the mixture contains x% alcohol and (100-x)% water.

i. Ratio of Alcohol to Water by Mass:

To calculate the ratio by mass, we need to know the densities of alcohol and water.

Density of Alcohol (ρalcohol) = ρ1
Density of Water (ρwater) = ρ2

Given that the density of the mixture (ρmixture) is 750 kg/m^3, we can use the formula:

ρmixture = (x/100) * ρ1 + ((100-x)/100) * ρ2

Since the density of a mixture is the mass per unit volume, we can rewrite this formula in terms of mass:

750 kg/m^3 = (x/100) * ρ1 + ((100-x)/100) * ρ2

To find the ratio of alcohol to water by mass, we divide the mass of alcohol by the mass of water:

Ratio by Mass = (x/100) * ρ1 / (100-x)/100 * ρ2 = (x/100) * ρ1 / (1 - x/100) * ρ2

ii. Ratio of Alcohol to Water by Volume:

To calculate the ratio by volume, we need to consider the volume fractions of alcohol and water in the mixture.

Let's assume that the volume fraction of alcohol is y, and the volume fraction of water is (1-y).

To calculate the ratio by volume, we use the following formula:

Ratio by Volume = y / (1 - y)

The volume fractions can be calculated from the mass fractions and the densities:

y = (x/100) * (ρ1 / ρmixture)
(1 - y) = ((100-x)/100) * (ρ2 / ρmixture)

Substituting these values, we have:

Ratio by Volume = (x/100) * (ρ1 / ρmixture) / ((100-x)/100) * (ρ2 / ρmixture)

Please provide the values of ρ1 and ρ2 (density of alcohol and water) to continue with the calculation.

To calculate the ratio of alcohol to water in the mixture, we need to consider both the mass and volume of the alcohol and water.

i. To calculate the ratio by mass:

1. Let's assume we have x amount of alcohol and y amount of water in the mixture.
2. The density of alcohol is typically around 789 kg/m^3, while the density of water is 1000 kg/m^3.
3. We can use the formula for density: density = mass/volume. Rearranging the formula, we have mass = density x volume.
4. Let's set up the equation for the total mass of the mixture: (x * density of alcohol) + (y * density of water) = (x + y) * 750 kg/m^3.
5. Simplify the equation: (x * 789 kg/m^3) + (y * 1000 kg/m^3) = (x + y) * 750 kg/m^3.
6. Now, you'll need another equation to determine the ratio. You can use the definition of the ratio: ratio = x/y.
7. Divide both sides of the previous equation by y: (x/y) * 789 kg/m^3 + 1000 kg/m^3 = 750 kg/m^3.
8. Rearrange the equation to isolate the ratio: (x/y) * 789 kg/m^3 = 750 kg/m^3 - 1000 kg/m^3.
9. Simplify: (x/y) * 789 kg/m^3 = -250 kg/m^3.
10. Divide both sides of the equation by 789 kg/m^3: x/y = (-250 kg/m^3) / (789 kg/m^3).
11. The ratio of alcohol to water by mass is approximately -0.317.

ii. To calculate the ratio by volume:

1. Let's assume we have V liters of alcohol and W liters of water in the mixture.
2. The density is given in kg/m^3, so we need to convert to kg/liter to match the volume units in the ratio.
- Density of alcohol: 789 kg/m^3 = 0.789 kg/liter
- Density of water: 1000 kg/m^3 = 1 kg/liter
- Density of the mixture: 750 kg/m^3 = 0.75 kg/liter
3. The equation for the total volume of the mixture is: V + W = (V + W) * 0.75 kg/liter.
4. Simplify the equation: V + W = 0.75V + 0.75W.
5. Rearrange the equation to isolate the ratio: V - 0.75V = 0.75W - W.
6. Simplify: 0.25V = 0.25W.
7. Divide both sides of the equation by 0.25: V/W = W/W.
8. The ratio of alcohol to water by volume is 1:1.

So, the ratio of alcohol to water in the mixture is approximately -0.317 by mass and 1:1 by volume.