Answers:
a. .20 Molar
b. .18 Molar
Explanation: Calculating the concentration of a solution is fundamental to future units of Chemistry so I hope my explanation will help!
The main formula that we will be using is the formula for Molarity or concentration of a solution which is (Moles of solute)/(Liters of solution). A mole is a unit of measurement used to measure the amount of a substance. There are 6.022*10^23 things in one mole. These things can be atoms or molecules etc.
In part A, we are given that there are .02 Moles in 100 ml of solutions. The .02 Moles are our Moles of solute. We have to convert the 100 ml of the solution to Liters to match our formula. Otherwise, our value would be too small. To convert from ml to L we simply divide by 1000 since there are 1000 ml in 1 Liter. This means that 100 ml is equal to .1 L. Now we can plug into our equation for molarity which gives us Molarity(concentration)=(.02)/(.1) which is .2. We call the concentration molar so the concentration is .2 molar.
In part B, there is one extra step we have to take. Instead of giving a value in moles, we are given a value in grams. To convert from grams to moles, we have to divide the grams of substance by its molar mass. To find the molar mass of KOH or Potassium Hydroxide, we have to look at the periodic table. Under K on the table, we will find its molar mass which is 39.0983. We then look for Oxygen and Hydrogen and see that their molar masses are 15.999 and 1.00783 respectively. We add all these values to find the molar mass of KOH. Suppose the molecule was H2SO4, we would multiply the molar mass of hydrogen by 2 and Oxygen by 4. The molar mass of KOH is 56.1056. To find the moles, we divide 5 grams by 56.1056 which gives us .089 Moles. We are given 500 ml of solution which we divide by 1000 to get .5 L. Now plugging into our Molarity equation we get (.089)/(.5) which gives us a .18 Molar solution.
Hope this helps!