Question

The solubility of salt at ${30^ \circ }C$ is $50.$ Calculate the weight of water required to prepare a saturated solution containing $90g$ of salt.
$A.$ $90g$
$B.$ $180g$
$C.$ $100g$
$D.$ $50g$

Answer 1

Solubility is a property referring to the ability of a given substance, the solute to dissolve in a solvent (In most of the cases the solvent is water). Solubility is measured in terms of the maximum amount of solute dissolve in a solvent at equilibrium.

Formula used: ${{Solubility of solute}}\left( {{{salt}}} \right) = \dfrac{{{W_{solute}}}}{{{W_{solvent}}}} \times 100$
Where, ${W_{solute}}$ is the weight of solute in saturated solution and ${W_{solvent}}$ is weight of solvent in saturated solution.

Complete step-by-step solution: In the given question it is given that the solubility of salt at ${30^ \circ }C$ is $50.$ we have to determine the weight of water required to prepare a saturated solution containing $90g$ of salt.
Now, given weight of salt $= 90g$
And solubility of salt $= 50$
By using the above formula we can determine the weight of water.
${{Solubility of solute}}\left( {{{salt}}} \right) = \dfrac{{{W_{solute}}}}{{{W_{solvent}}}} \times 100$
By putting the value of known quantity that is weight of salt and solubility, we get
$50 = \dfrac{{90}}{{{W_{solvent}}}} \times 100$
On solving the above equation, we will get the value of the weight of water.
${W_{solvent}} = \dfrac{{90}}{{50}} \times 100$
$\Rightarrow$ ${W_{solvent}} = 180g$
Therefore, $180g$ of water required to prepare a saturated solution containing $90g$ of salt.

So, the correct option is $B.$

Note: These are the parameters that affect the solubility of a solute in a solvent namely, temperature, and pressure.
Temperature: The solubility of a solute is directly proportional to the temperature that is higher the temperature of solvent the greater the solubility of the solute. There is an exception gaseous solute dissolve less in hotter liquid solvents than in colder solvents.
Pressure: Generally pressure does not affect the solubility of most solutes in a solvent but in the case gaseous solute dissolve more liquid solvents at higher pressures than at lower pressures.