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Question: \(3{\text{ grams}}\)of salt of molecular weight \(30\) is dissolved in \(250{\text{ g}}\) of water. ...

3 grams3{\text{ grams}}of salt of molecular weight 3030 is dissolved in 250 g250{\text{ g}} of water. Find the molality of the solution. (Multiply the answer by 10{\text{10}})

Explanation

Solution

The molality can be defined as the number of moles of solute present per kilogram of solvent. One can find out the number of moles by the data given in the question. One can calculate the molality by putting in the relevant values in the equation. There should be multiplication by 10{\text{10}} to the final molality value as specified in the question.

Complete step by step answer: 4
-First of all let's understand the concept of molality where it is a property of a solution and is defined as the number of moles of solute per kilogram of solvent.
-Now let's analyze the given values in the question and move forward to calculate the molality. The total mass of salt is given which is 3 grams3{\text{ grams}} and the molecular weight of salt is given which is 30{\text{30}}. Now by using this data we can calculate the number of moles of salt by using the following formula,
Number of moles of salt = Total mass of saltMolecular weight of salt=330=0⋅1 moles{\text{Number of moles of salt = }}\dfrac{{{\text{Total mass of salt}}}}{{{\text{Molecular weight of salt}}}} = \dfrac{3}{{30}} = 0 \cdot 1{\text{ moles}}
-Now that we have got the value of the number of moles we can calculate the value of molality by using the following formula,
Molality=Number of molesMass of solvent(water) in kg=0⋅10⋅250=0⋅4 mol/kgMolality = \dfrac{{{\text{Number of moles}}}}{{{\text{Mass of solvent(water) in kg}}}} = \dfrac{{0 \cdot 1}}{{0 \cdot 250}} = 0 \cdot 4{\text{ mol/kg}}
Therefore, the molality of salt which is dissolved in water is 0⋅4 mol/kg0 \cdot 4{\text{ mol/kg}}.
-But we need to multiply the answer by 10{\text{10}} as specified in the question we get the final value as 44. Hence, 44 is the final answer.

Note: While calculating the molality one should remember that the values given should be taken in the equation as per specific units which is SI{\text{SI}} and relevant conversions should be done to avoid error in answer. The unit for molality is mol/kg{\text{mol/kg}} and sometimes molal{\text{molal}} is used where both are valid units of molality. The value of molality only depends on the mass of solute and mass of solvent which is the primary advantage of using molality to measure concentration.