Question

500g tooth paste sample has 0.2g fluoride ion concentration. What is the concentration of fluoride in terms of ppm level?

Answer 1

Parts per million is a way of expressing very dilute concentrations of substances. Just like percent which means out of hundred, parts per million means out of a million. We can find out the fluoride concentration using the formula in which a part of the component is divided by the total parts of the component followed by a multiplication of ten to the power six.

Formula used: $concentration\,\,in\,\,ppm = \dfrac{{weight\,\,of\,\,ion}}{{weight\,\,of\,\,paste}} \times {10^6}$

Complete step-by-step answer:
The unit parts per million depends on the mass of any substance present in wither 1 litre of solvent or amount of paste or solvent. Although it includes litres in its general formula, yet we calculate it as the number of particles found per litre of the solvent, so the volume remains constant. It is used for infinitesimally small concentrations and thus a small change in temperature does not affect the concentration in ppm.
Let us write the formula which is used to calculate the concentration of any ion in terms of parts per million. It is expressed in terms of weight by weight.
$concentration\,\,in\,\,ppm = \dfrac{{weight\,\,of\,\,ion}}{{weight\,\,of\,\,paste}} \times {10^6}$
We are given the weight of fluoride ion concentration as 0.2g and the weight of toothpaste as 500gms. Putting these values in the above formula, we can determine the concentration of fluoride in terms of ppm level.

$$concentration\,\,in\,\,ppm = \dfrac{{0.2}}{{500}} \times {10^6} \\\ \therefore concentration\,\,in\,\,ppm = 400ppm \\\$$

The concentration of fluoride in a 500g toothpaste sample containing 0.2g fluoride ion concentration in terms of ppm level is 400ppm.

Note: We learnt that ppm concentration remains unaffected by change in temperature as volume is constant in them. But if we talk about other concentration units such as molarity, it does change with temperature because the mass of a substance changes with its volume and so the concentration also changes.