Anthony T. answered • 03/30/22
Patient Science Tutor
First, let's calculate the number of grams of NaOH needed to make 3 L of 0.3 M solution. The calculation is 0.3 moles / L x 3 L x 40 g / mole = 36 g NaOH needed.
The stock solution has a density (ρ) of 1200 g /L of which 30% is NaOH by mass. The mass of NaOH per mL is 1200 g/L x 1L / 1000 mL x 0.30 = 0.36 g/ mL or taking the reciprocal 2.78 mL / g NaOH.
Finally, 2.78 mL / g x 36 g NaOH = 100.08 mL or about100 mL of stock solution.
Anthony T.
Molarity is number of moles per liter of solution. If you have 3 L then you have 3 times as many moles (0.3 x 3). To convert to grams you have to use he conversion factor of moles NaOH to grams. Using the periodic table you find that there are 40 grams of NaOH for every mole of NaOH, so you need to multiply the number of moles NaOH by the molar mass of NaOH (0.3 x 3 x 40). We determined that the stock solution has 0.36 g NaOH for every mL of solution, so when you take the reciprocal of 0.36 g/mL, you get how many mL of the solution contain 1 gram of NAOH. Multiplying that result by the number of grams we need from the first part (36 g) gives you the number of mL you need to take. ( 1 / 0.36 g / mL x 36 g) where 1 / 0.36 g/mL = 2.78 mL / g is the reciprocal of 0.36 g / mL. When you take the reciprocal of a ratio like g / mL, you get mL / g. I hope this helps.03/31/22
Koyuki M.
how did you get 0.36g? and where did mL come from? "We determined that the stock solution has 0.36 g NaOH for every mL of solution" what does, "taking the reciprocal" mean? (to get to 2.78 mL / g NaOH".)03/31/22
Anthony T.
"The stock solution has a density (ρ) of 1200 g /L of which 30% is NaOH by mass. The mass of solution per mL is 1200 g/L x 1L / 1000 mL x 0.30 = 0.36 g/ mL ". There are 1200 g for every liter, but a liter is 1000 mL, so by dividing 1200 g by 1000 mL gives you the number of grams per each mL. Since the NaOH is 30% by mass, you have to multiply 1200 g/1000 mL by 0.3 to get the mass of NaOH per each mL which comes out to be 0.36 g NaOH per mL.03/31/22
Koyuki M.
I still dont understand what does, "taking the reciprocal" mean? (to get to 2.78 mL / g NaOH".) and the logic behind the last calculation, 2.78 mL / g x 36 g NaOH = 100.08 mL Thank you for being patient with me! and your help, it really means a lot to me to have someone helping me like this.04/01/22
Anthony T.
Here is an analogy. Your car gets 35 miles on one gallon of gas (35 m/g.) This can be written 35 m / 1 g where 35 m is in the numerator of the fraction and 1 g is in the denominator. Now we want to know how many gallons will it take to go one mile? If we take the reciprocal of the fraction ( 1 g / 35 m), we can answer that question by dividing 1 g by 35 m which gives us 0.0286 gallons to go one mile (g/m). Now we want to know how much gas I will use to go 100 miles. Multiply 0.0286 g / m x 100 m = 2.86 gallons of gas. Notice that the miles unit (m) will cancel out as the m unit is in both the numerator and denominator leaving only g as the remaining unit. This is called dimensional analysis and is a handy way to check if your answer makes sense. This is the same reasoning employed in the problem. I hope this makes sense.04/03/22
Koyuki M.
can you please explain this part ; "The calculation is 0.3 moles / L x 3 L x 40 g / mole = 36 g NaOH needed." what is the formula (in words, like mass, volume, moles, etc. if that makes sense) you used? nd also this part; why did 0.36 become 2.78? "taking the reciprocal 2.78 mL / g NaOH." Thank you in advance03/31/22