<u>Answer:</u> The final concentration of potassium nitrate is
<u>Explanation:</u>
To calculate the molecular mass of solute, we use the equation used to calculate the molarity of solution:
![\text{Molarity of the solution}=\frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20the%20solution%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solute%7D%5Ctimes%201000%7D%7B%5Ctext%7BMolar%20mass%20of%20solute%7D%5Ctimes%20%5Ctext%7BVolume%20of%20solution%20%28in%20mL%29%7D%7D)
We are given:
Mass of potassium nitrate (solute) = 0.360 g
Molar mass of potassium nitrate = 101.1 g/mol
Volume of solution = 500.0 mL
Putting values in above equation, we get:
![\text{Molarity of }KNO_3=\frac{0.360\times 1000}{101.1\times 500.0}\\\\\text{Molarity of }KNO_3=7.12\times 10^{-3}M](https://tex.z-dn.net/?f=%5Ctext%7BMolarity%20of%20%7DKNO_3%3D%5Cfrac%7B0.360%5Ctimes%201000%7D%7B101.1%5Ctimes%20500.0%7D%5C%5C%5C%5C%5Ctext%7BMolarity%20of%20%7DKNO_3%3D7.12%5Ctimes%2010%5E%7B-3%7DM)
To calculate the molarity of the diluted solution, we use the equation:
.......(1)
- <u>Calculating for first dilution:</u>
are the molarity and volume of the concentrated
solution
are the molarity and volume of diluted
solution
We are given:
![M_1=7.12\times 10^{-3}M\\V_1=10mL\\M_2=?M\\V_2=500.0mL](https://tex.z-dn.net/?f=M_1%3D7.12%5Ctimes%2010%5E%7B-3%7DM%5C%5CV_1%3D10mL%5C%5CM_2%3D%3FM%5C%5CV_2%3D500.0mL)
Putting values in equation 1, we get:
![7.12\times 10^{-3}\times 10=M_2\times 500\\\\M_2=\frac{7.12\times 10^{-3}\times 10}{500}=1.424\times 10^{-4}M](https://tex.z-dn.net/?f=7.12%5Ctimes%2010%5E%7B-3%7D%5Ctimes%2010%3DM_2%5Ctimes%20500%5C%5C%5C%5CM_2%3D%5Cfrac%7B7.12%5Ctimes%2010%5E%7B-3%7D%5Ctimes%2010%7D%7B500%7D%3D1.424%5Ctimes%2010%5E%7B-4%7DM)
- <u>Calculating for second dilution:</u>
are the molarity and volume of the concentrated
solution
are the molarity and volume of diluted
solution
We are given:
![M_2=1.424\times 10^{-4}M\\V_2=10mL\\M_3=?M\\V_3=250.0mL](https://tex.z-dn.net/?f=M_2%3D1.424%5Ctimes%2010%5E%7B-4%7DM%5C%5CV_2%3D10mL%5C%5CM_3%3D%3FM%5C%5CV_3%3D250.0mL)
Putting values in equation 1, we get:
![1.424\times 10^{-4}\times 10=M_3\times 250\\\\M_3=\frac{1.424\times 10^{-4}\times 10}{250}=5.70\times 10^{-6}M](https://tex.z-dn.net/?f=1.424%5Ctimes%2010%5E%7B-4%7D%5Ctimes%2010%3DM_3%5Ctimes%20250%5C%5C%5C%5CM_3%3D%5Cfrac%7B1.424%5Ctimes%2010%5E%7B-4%7D%5Ctimes%2010%7D%7B250%7D%3D5.70%5Ctimes%2010%5E%7B-6%7DM)
Hence, the final concentration of potassium nitrate is