Question

Near room temperature the density ofwater is 1 g/ml and the densityof ethanol is 0.789 g/ml . What volume of ethanol contains the same number ofmolecules as are present in 175 ml of h2o?

Answer 1

Answer: 566.7 ml

Explanation:-

`Density=(mass)/(Volume)`

Density of the water=
`1g/ml`

volume of water = 175 ml

Putting in the values we get:

`1g/ml=(mass)/(175ml)`

mass of water = 175 g

According to avogadro's law, 1 mole of every substance occupies 22.4 L at STP and contains avogadro's number
`6.023* 10^(23)` of particles.

tex]\text{Number of moles of water}=\frac{175g}{18g/mol}=9.72moles[/tex]

Thus 9.72 moles of ethanol are required.

Mass of ethanol=
`moles* {\text {Molar mass}}=9.72* 46=447.12g`

`Density=(mass)/(Volume)`

Density of ethanol=
`0.789g/ml`

volume of ethanol= ?

Putting in the values we get:

`0.789g/ml=(447.12g)/(Volume)`

`Volume=566.7ml`

Thus volume of ethanol that contains the same number of molecules as are present in 175 ml of water is 566.7 ml.

Answer 2

Step-by-step explanation:

As we know that density is the amount of mass present in a liter of solution.

Mathematically, density =
`(mass)/(volume)`

As it is given that density of water is 1 g/ml and volume is 175 mL. So, mass of water will be calculated as follows.

density =
`(mass)/(volume)`

1 g/ml =
`(mass)/(175 ml)`

mass = 175 g

It is known that 18 g of water contains 1 mole of water. Hence, number of moles present in 175 g of water will be calculated as follows.

No. of moles =
`\frac{mass}{\text{molar mass}}`

=
`(175 g)/(18 g/mol)`

= 9.72 mol

This means that we have 9.72 moles of ethanol also.

Hence, volume of ethanol present in 175 ml of water will be as follows.

No. of moles of ethanol =
`\frac{density * Volume}{\text{molar mass of ethanol}}`

9.72 mol =
`(0.789 g/ml * Volume)/(46 g/mol)`

Volume = 566.69 ml

Thus, we can conclude that 566.69 ml volume of ethanol contains the same number of molecules as are present in 175 ml of
`H_(2)O`.