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:-

$Density=\frac{mass}{Volume}$

Density of the water= $1g/ml$

volume of water = 175 ml

Putting in the values we get:

$1g/ml=\frac{mass}{175ml}$

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 $6.023\times 10^{23}$ 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=$moles\times {\text {Molar mass}}=9.72\times 46=447.12g$

$Density=\frac{mass}{Volume}$

Density of ethanol= $0.789g/ml$

volume of ethanol= ?

Putting in the values we get:

$0.789g/ml=\frac{447.12g}{Volume}$

$Volume=566.7ml$

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

Explanation:

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

Mathematically,     density = $\frac{mass}{volume}$

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 = $\frac{mass}{volume}$

                  1 g/ml = $\frac{mass}{175 ml}$

                   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 = $\frac{mass}{\text{molar mass}}$

                                       = $\frac{175 g}{18 g/mol}$

                                       = 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 = $\frac{density \times Volume}{\text{molar mass of ethanol}}$

                9.72 mol = $\frac{0.789 g/ml \times Volume}{46 g/mol}$

                 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 $H_{2}O$.