A garden fertilizer contains 15% by mass of nitrogen. The recommended usage is 30g of fertilizer per 10dm^3 of water. What is the concentration of nitrogen in this solution?

a)0.15 g dm^-3
b)0.30 g dm^-3
c)0.45 g dm^-3
d)3.00 g dm^-3

15% by mass means 15 g N/100g fertilizer or 0.15 g N/g fertilizer.

So 30 g fertilizer has 30 x 0.15 = 4.50g N. You put this in 10 dm^3 so the concn is
4.50g/10dm^3 = 0.45 g/dm^3

To find the concentration of nitrogen in the solution, we need to determine the amount of nitrogen present in the given amount of fertilizer.

First, let's calculate the amount of nitrogen in 30g of fertilizer. Since the fertilizer contains 15% nitrogen by mass, we can find the mass of nitrogen by multiplying the mass of the fertilizer by the percentage of nitrogen:

Mass of nitrogen = 30g * 0.15 = 4.5g

Now, let's calculate the volume of the solution. We are given that 30g of fertilizer is dissolved in 10dm^3 of water. Therefore, the volume of the solution is 10dm^3.

Finally, we can find the concentration of nitrogen by dividing the mass of nitrogen by the volume of the solution:

Concentration of nitrogen = Mass of nitrogen / Volume of solution
Concentration of nitrogen = 4.5g / 10dm^3

Converting from grams to grams per cubic decimeter (g dm^-3), we get:

Concentration of nitrogen = 0.45 g dm^-3

Therefore, the concentration of nitrogen in this solution is c) 0.45 g dm^-3.