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Question: Given,\(5\times {{10}^{-3}}kg\) of urea is dissolved in\(2\times {{10}^{-3}}kg\) of water. Calculate...

Given,5×10−3kg5\times {{10}^{-3}}kg of urea is dissolved in2×10−3kg2\times {{10}^{-3}}kg of water. Calculate the percent by mass of urea (2M)

Explanation

Solution

To solve this question we will use the formula of per cent by mass and it is calculated as the mass of the solute divided by mass of the solution (Solute + solvent) multiply by 100%. It is given asww\dfrac{w}{w}%=\dfrac{m}{M}\times 100. Urea is the solute and water is the solvent in this question.

Complete answer:
From your chemistry lessons you have learned about the mass percentage or per cent by mass. Mass percent is a way of expressing the concentration.
Percent by mass is mainly used to describe the component present in the particular mixture. It helps us to determine the mass of solute present in the given mass of the solution. And the quantity of the solute is expressed in mass or maybe by moles.
So, the formula of percent by mass is defined as the mass of solute divided by the total mass of the solution multiplied by 100 % and it is given as:
ww\dfrac{w}{w}% = mM×100\dfrac{m}{M}\times 100 ………………. (1)
Where,ww\dfrac{w}{w}%= percent by mass
mm = mass of the solute
MM = mass of the solution
Now, the mass of the solution = mass of solute + mass of solvent
In the question the mass of the urea which is a solute is given as5×10−3kg5\times {{10}^{-3}}kg and the mass of the solvent (Water) is given as2×10−3kg2\times {{10}^{-3}}kg. Therefore the mass of the solution= mass of urea + mass of water.
So, the mass of solution =5×10−3+2×10−3=7×10−3kg5\times {{10}^{-3}}+2\times {{10}^{-3}}=7\times {{10}^{-3}}kg
Now, put the values in the equation (1), we will get:
ww\dfrac{w}{w}% = 5×10−32×10−3×100 \dfrac{5\times {{10}^{-3}}}{2\times {{10}^{-3}}}\times 100
ww\dfrac{w}{w}% = 71.4%

Thus, the percent by mass of Urea is 71.4%.

Note:
Like percent by mass there is percent by volume also which is defined as the volume of solute divided by the volume of the solution multiplied by 100%. The units of the all the concentration terms should be the same if the mass of solute is in Kg or in g then the unit mass of solution or mass of solvent should also be in kg or g.