Question

If a solution is 0.5% $\text{(w/v)}$ , how many $\text{mg/ml}$ is that?

Answer 1

Hint: The conversion of gram to milligram is done by multiplying the gram value with thousand.
The $\text{(w/v)}$ ratio is the weight by volume percentage of the sample, which is used to represent the concentration.
$\text{Weight by}\text{volume }$

Complete step by step answer:
- So in the question it is as that for a solution of 0.5% given in weight by volume percentage is equal to how many . Before going into the solution part we should know some basic ideas of these concentration terms, what does they really mean.
- Weight by volume percentage is the percentage of the ratio of the weight of solute present in the sample in a volume of 100 mL of the solution and by this definition we know that this parameter is used for solving the problems related to concentration.
- In the question it is given that the weight by volume percentage of the given sample is about 0.5 % and if we converted it into gram per milliliter then, 0.5 % of the sample is equal to 0.5 g of solute present in 100mL of the solution, i.e. $\text{0}\text{.5 }$
So now we know 100mL of solution contains 0.5g of solute and we have to solve for 1mL of solution,
$\text{1ml=}{\displaystyle \frac{\text{0}\text{.5}}{\text{100}}}\text{=0}\text{.005g}$
Hence now we know that the 1 ml of solution consists of 0.005 g of the solute.
All the values obtained till are in gram and in milliliter. We are supposed to find the values in milligram and milliliter. So let’s convert the gram to milligram.
- We know the conversion that:
$\text{1g=1}{\text{0}}^{\text{3}}\text{mg=1000mg}$
Hence, $\text{0}\text{.005g }\times {\displaystyle \frac{\text{1000mg}}{\text{1g}}}\text{=5mg}$
So finally we got the value in milligram for 1 mL of the solution. As we solved for 1 milliliter of the solution, we could represent the obtained value as, $\text{5mg/ml}$

Note: Caution should be taken when doing the calculation and rounding off to significant figures and the interconversion of the units should be learnt very thoroughly to solve such problems.
- Problems may come where we have to convert the milligram to percentage, so always study a standard equation and alter it to get various equations, it may help to minimize confusions.
- The weight by volume ratio is also represented as the mass by volume ratio and the percentage is said as the mass by volume percentage and is represented as $\left({}^m/{}_v\right)$