Question

A solution is prepared by dissolving 15.0 g of nh3 in 250.0 g of water. the density of the resulting solution is 0.974 g/ml. the molarity of nh3 in the solution is ________ m.

Answer 1

To solve this problem, first we assume the volume is purely additive. The density of the mixture can then be calculated by the summation of mass fraction of each component divided by its individual density:

1 / ρ mixture = (x NH3 / ρ NH3) + (x H2O / ρ H2O)                        ---> 1

Calculating for mass fraction of NH3:

x NH3 = 15 g / (15 g + 250 g)

x NH3 = 0.0566

Therefore the mass fraction of water is:

x H2O = 1 – x NH3 = 1 – 0.0566

x H2O = 0.9434

Assuming that the density of water is 1 g / mL and substituting the known values back to equation 1:

1 / 0.974 g / mL = [0.0566 / (ρ NH3)] + [0.9434 / (1 g / mL)]

ρ NH3 = 0.680 g / mL

Given the density of NH3, now we can calculate for the volume of NH3:

V NH3 = 15 g / 0.680 g / mL

V NH3 = 22.07 mL

The number of moles NH3 is: (molar mass NH3 is 17.03 g / mol)

n NH3 = 15 g / 17.03 g / mol

n NH3 = 0.881 mol

Therefore the molarity of NH3 in the solution is:

Molarity = 0.881 mol / [(22.07 mL  + 250 mL) * (1L / 1000 mL)

M = 3.238 mol/L = 3.24 M

Answer 2

The molarity of the ammonia solution of density 0.974 g/ml has been 3.32 M.

Density can be defined as mass per unit volume. The density of the given ammonia solution is 0.974 g/ml.

The mass of ammonia solution = mass of ammonia + mass of water

Mass of ammonia solution = 15 g + 250 g

Mass of ammonia solution = 265 grams

Volume of the solution can be given by;

$\rm \bold{Volume}\;=\;\dfrac{Mass}{Density}$

Volume of Ammonia solution = $\rm \dfrac{265}{0.974}$

Volume of Ammonia solution = 272.073 ml.

The molecular weight of ammonia is 17.031 g/mol

Molarity can be defined as moles of solute in a liter of solution. Molarity can be expressed as:

$\rm \bold{Molarity}\;=\;\dfrac{weight}{molecular\;weight}\;\times\;\dfrac{1000}{Volume\;(ml)}$

$\rm \bold{Molarity}\;=\;\dfrac{15}{17.031}\;\times\;\dfrac{1000}{265}$

Molarity = 0.88 $\times$ 3.773 M

Molarity = 3.32 M

The molarity of the ammonia solution of density 0.974 g/ml has been 3.32 M.

For more information about the molarity of a solution, refer to the link:

https://brainly.com/question/568905