I still don't get this problem!

Toxic chemicals in drinking water usually are reported and a safety level specified in units of parts per million (ppm) by mass. What is the molar concentration of arsenic in a water sample that has 1ppm arsenic (As)?

My teacher's work:

(1g As/1x10^6 g soln) x (1 mol As/74.92 g As) x (1 g soln/mL) x (1.0 x10^3 mL/1L)= 1x10^-5 mol As/L soln

Where did the 1 g As/1x10^6 g soln and 1g soln/1mL come from?

One ppm is one millionth of a gram or in simpler terms, 10^6.

The values of 1 g As/1x10^6 g soln and 1g soln/1mL are conversion factors that are used to convert between different units in the calculation.

Let's break down the calculation step by step:

(1g As/1x10^6 g soln) is the conversion factor used to convert from parts per million (ppm) to moles. In this case, we assume that the water sample contains 1 ppm of arsenic. This means that there is 1 gram of arsenic in 1 million grams of solution (soln). By dividing the amount of arsenic by the total amount of solution, we get the molar concentration of arsenic.

(1 mol As/74.92 g As) is the molar mass of arsenic. It tells us that for every 74.92 grams of arsenic, there is 1 mole of arsenic. This conversion factor is used to convert the mass of arsenic to moles.

(1 g soln/mL) is the conversion factor used to convert from grams of solution to milliliters of solution. It assumes that 1 gram of solution has a volume of 1 milliliter.

(1.0 x10^3 mL/1L) is the conversion factor used to convert from milliliters to liters. It assumes that there are 1000 milliliters in 1 liter.

By multiplying all these conversion factors together, we can convert from parts per million to moles per liter (mol/L), which gives us the molar concentration of arsenic in the water sample.

So, in summary, the values of 1 g As/1x10^6 g soln and 1g soln/1mL are used as conversion factors to convert between different units in the calculation.