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Quantitative Reasoning – Passage Based – Aqueous solutions and their Concentration!

2014_QNR 12. When solids, liquids or gases are dissolved in a liquid they make a solution. The substance (solid, liquid or gas) being dissolved is called the solute and the liquid that does the dissolving is called the solvent. Solutions which use water as the solvent are called aqueous solutions. When you dissolve a spoon of instant coffee in hot water or add water to some cordial syrup, you are making an aqueous solution.
The concentration of an aqueous solution refers to the amount of solute that has been dissolved in a fixed amount of water. For example, if a saline solution (made from salt dissolved in water) has a concentration of 10 g/L, then we know that 10g salt has been dissolved in 1 litre of water solvent.

The concentration of a solution can also be described by the proportion of the solute to solution either by mass or by volume.
The by mass concentration is used when a solid is dissolved in a solvent. This is calculated by dividing the mass of the solute (in grams) by the mass of the solution (also in grams) and the result converted into a percentage. It is important to note that the mass of the solution is equal to the mass of the solute plus the mass of the solvent. One millilitre of water has a mass of 1 gram.
When the solute is a liquid, the by volume concentration is used. In this case, the volume of the solute is divided by the volume of the solution and the result is again converted into a percentage. It does not matter which volume units (millilitres, litres or cubic centimetres) are used, provided that the same unit is used for both the solute and the solution.
(i) The table below indicates how much sugar can be found dissolved in different beverages.

2014_QNR 12_1

(i)Which of the following statements is true?

(1) Pure vegetable juice and orange juice have the same sugar concentration.

(2) Orange juice has a higher sugar concentration than apple drink.

(3) Soft drink has a lower sugar concentration than apple drink.

(4) Pure apple juice has a higher sugar concentration than soft drink.
(ii) How many grams of sugar must you add to 400 mL of water in order to make a sugar solution with a concentration of 10 g/L ?
(1) 40

(2) 2.5

(3) 4

(4) 25
(iii) When a saline solution is made by dissolving 6 g of salt in 50 mL of water, the concentration by mass of this solution is closest to

(1) 12%

(2) 0.1%

(3) 3%

(4) 11%

(iv) An aqueous solution of copper sulphate was left out in the hot sun. The heat caused some of the water to evaporate from the solution. The original 150 g solution had a concentration of 10% by mass. If the remaining solution has a concentration of 15% by mass, what volume of water evaporated ?
(1) 100 mL

(2) 10 mL

(3) 15 mL

(4) 50 mL

Ans:

(i)  The below chart gives us the sugar concentration for various types of drink:

Type of drink Amount of drink
(common size)
Sugar content
(gm or ml)
Sugar conc.
Soft drink 375 mL 40-45 gm 40*100/375  to 45*100/375
or, 10.6% to 12%
Apple drink
(25% pure apple;
75% water)
250 mL 25 gm 25*100/250 =10%
100% pure
orange juice
250 mL 25 gm 25*100/250=10%
100% pure
vegetable juice
250 mL 10-15 gm 10*100/250 to 15*100/250%
or, 4% to 6
Water 600 mL 0 0

Now, let us look at each of the answer options:

(1) Pure vegetable juice and orange juice have the same sugar concentration. –> Pure vegetable juice has sugar concentration range from 4% to 6% but orange juice has 10%. Incorrect option.

(2) Orange juice has a higher sugar concentration than apple drink.  –> Both have sugar concentration as 10%. Incorrect option.

(3) Soft drink has a lower sugar concentration than apple drink. –> Soft drink has sugar concentration range from 10.6% to 12 % but apple drink has 10%. Incorrect option.

(4) Pure apple juice has a higher sugar concentration than soft drink. –> Correct option. All others are incorrect.

Suppose, we had a question asking the sugar concentration of pure apple juice, we would calculate it as:

Apple drink has 25% pure apple and 75% water => 250 ml volume has 1/4th pure apple juice.

Since 3/4 of the solution accounting for volume of water does not have any sugar; 250/4 ml of pure apple juice contributes the 25 gm sugar. Sugar concentration = 25*100/(250/4)= 40%.

 (ii) 

1 L of solution has 10 gm sugar
Sugar concentration= [10/1000]*100 =1 %

Let ‘m’ be the grams of sugar must be added to 400 ml of water
Total solution: m + 400

As per the question= m*100/(m+400) =1 [equating the concentration in both the cases].
=> 100m = m+ 400
=> 99m = 400
=> m~ 4 gm. Option (3)

(iii) Concentration by mass= mass of salt*100/ total mass = [6/(50+6)]*100. Although the calculation is straight forward let us learn some techniques to solve this or any other similar expressions:

First calculation method:
———————————-
(6/56) > (6/60)

=>(6*100/56) > (6*100/60)

=>(6*100/56) >10

 

Similarly,

(6/56) < (6/50)

=>(6*100/56) < (6*100/50)

=>(6*100/56) <12

Concentration is greater than 10% and lesser than 12%. Option (4)

Second calculation method:
—————————————–

The question is “How much percentage is 6 out of 56”?

10% of 56 = 5.6. So, the answer must be little greater than 10%.
1% of 56 = 0.56.
Adding the two we get 11% of 56 as 6.16. Answer option (4).

 (iv) 

Since only water has evaporated, the copper sulphate quantity remains same.

In first case, CuSO4 quantity = 10% of 150 g = 15 gm

In the second case, concentration has become 15% by mass. Since quantity of solute remains same,
15% of the “remaining solution” = 15 gm. [equating the solute content]
“Remaining solution” = 100 gm.

Initial solution = 150 gm. 50 gm of water has evaporated. Option (4)

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