Question

How many grams of acetic acid should be dissolved in 100.0 g of water to make a 4.0 percent (by mass solution of vinegar?

Answer 1

Use the formula of mass percent and find a relation in the mass of acetic acid added and the mass percent which is given in the question, then solve for the unknown variable.

Complete answer:
In order to answer the question, we need to know about moles and molar mass. Now, matter is made up of atoms, and as matter has mass, then the atoms should have an individual mass. Molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ particles. For, example, the hydrogen molecule has a molar mass of 2 grams. This means 2 grams of hydrogen contains $6\times {{10}^{23}}$atoms, and this number is also called the Avogadro’s number.
Number of moles of an element or a compound is the ratio of its given mass taken by the user, to its molar mass. More is the number of moles, more is the concentration of the substance. Now, let us come to the question. Mass percent is the percentage of solute present by mass. Let us take the mass of acetic acid to be “x”. If the acetic acid is added to the solution, the total mass of the solution will increase. Using this concept we will try to solve the question. So, by using the formula of mass percent, we have:
$mass\,percent=\dfrac{mass\,solute}{mass\,solution}\times 100$
Now, it is to be noted that if x grams of acetic acid are added, then the mass of the solution will be $(100+x)g$. So, we continue our calculation:

& 4=\left( \dfrac{x}{100+x} \right)\times 100 \\\ & \Rightarrow 4\times (100+x)=100x \\\ & \Rightarrow 96x=400 \\\ & \Rightarrow x=\dfrac{400}{96}=4.1667 \\\ \end{aligned}$$ So, we get the mass of acetic acid which is added into the solution to be approximately 4.2 grams. **Note:** It is to be noted that this solution, which contains water and approximately 4 percent of acetic acid, is also known as vinegar which is used for household cooking purposes.