What is the solubility of sodium chloride in 30 C water

Text Solution

Solution : The molecular mass of NaCl = 23 + 35.5 ` " " = 58.5` ` " " ` The solubility of NaCl = 6.150 mol/L ` " " = 6.150 xx 58.5` ` " " =359 . 8 g//L` The mass of NaCl dissolved in ` 100 cm ^(3) ` of water ` " " = (359.8 )/(1000) xx 100` ` " " = 35. 98 g ` Since , 80 g of NaCl is dissolved in ` 100 cm ^(3)` of water the amount of undissolved NaCl = 80 - 35.9 8 = 44.02 g. Additions of additional ` 50 cm ^(3)` of water will dissolve some more undissolved NaCl . Total volume now becomes ` 150 cm ^(3)` Hence , the mass of NaCl dissolved in ` 150 cm ^(3)` water ` " " = ( 159. 8)/( 1000) xx 150 = 53. 97 g ` The mass of NaCl still remained undissolved ` " " = 80 - 53. 97 = 26. 03 g `

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The solubility of a substance is the amount of that substance that is required to form a saturated solution in a given amount of solvent at a specified temperature. Solubility is often measured as the grams of solute per $100 \: \text{g}$ of solvent. The solubility of sodium chloride in water is $36.0 \: \text{g}$ per $100 \: \text{g}$ water at $20^\text{o} \text{C}$. The temperature must be specified because solubility varies with temperature. For gases, the pressure must also be specified. Solubility is specific for a particular solvent. In this section, we will consider solubility of material in water as solvent.

The solubility of the majority of solid substances increases as the temperature increases. However, the effect is difficult to predict and varies widely from one solute to another. The temperature dependence of solubility can be visualized with the help of a solubility curve, a graph of the solubility vs. temperature (see figure below).

Figure $\PageIndex{1}$: Solubility curves for several compounds.

Notice how the temperature dependence of $\ce{NaCl}$ is fairly flat, meaning that an increase in temperature has relatively little effect on the solubility of $\ce{NaCl}$. The curve for $\ce{KNO_3}$, on the other hand, is very steep, and so an increase in temperature dramatically increases the solubility of $\ce{KNO_3}$.

Several substances—$\ce{HCl}$, $\ce{NH_3}$, and $\ce{SO_2}$—have solubility that decreases as temperature increases. They are all gases at standard pressure. When a solvent with a gas dissolved in it is heated, the kinetic energy of both the solvent and solute increase. As the kinetic energy of the gaseous solute increases, its molecules have a greater tendency to escape the attraction of the solvent molecules and return to the gas phase. Therefore, the solubility of a gas decreases as the temperature increases.

Solubility curves can be used to determine if a given solution is saturated or unsaturated. Suppose that $80 \: \text{g}$ of $\ce{KNO_3}$ is added to $100 \: \text{g}$ of water at $30^\text{o} \text{C}$. According to the solubility curve, approximately $48 \: \text{g}$ of $\ce{KNO_3}$ will dissolve at $30^\text{o} \text{C}$. This means that the solution will be saturated since $48 \: \text{g}$ is less than $80 \: \text{g}$. We can also determine that there will be $80 - 48 = 32 \: \text{g}$ of undissolved $\ce{KNO_3}$ remaining at the bottom of the container. In a second scenario, suppose that this saturated solution is heated to $60^\text{o} \text{C}$. According to the curve, the solubility of $\ce{KNO_3}$ at $60^\text{o} \text{C}$ is about $107 \: \text{g}$. The solution, in this case, is unsaturated since it contains only the original $80 \: \text{g}$ of dissolved solute. Suppose in a third case, that the solution is cooled all the way down to $0^\text{o} \text{C}$. The solubility at $0^\text{o} \text{C}$ is about $14 \: \text{g}$, meaning that $80 - 14 = 66 \: \text{g}$ of the $\ce{KNO_3}$ will recrystallize.

Summary

The solubility of a substance is the amount of that substance that is required to form a saturated solution in a given amount of solvent at a specified temperature.
A solubility curve is a graph of the solubility vs. temperature
The solubility of a solid in water increases with an increase in temperature.
Gas solubility decreases as the temperature increases.

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Answer

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Hint: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.