"a 10.0 ml sample of this solution was transferred to a 500.0-ml volumetric flask and diluted to the mark with water. then 10.0 ml of the diluted solution was transferred to a 250.0-ml flask and diluted to the mark with water. what is the final concentration of the kno3 solution? "

If the original solution is "X" M in KNO₃ (moles/Lt), then final solution will be in concentration (2/250)×X M

Explanation:

Original solution of KNO₃ is X M, then, we take a sample of 10 ml and transferre it to 500 ml:

1000ml=X moles KNO₃

10ml=1/100 X moles KNO₃, that will be in 500ml

We then take 10 ml of this new solution and transferre it to a flask with a final volume of 250ml, so:

500ml=(1/100) X moles KNO₃

10ml=(1/5000) X moles KNO₃, these moles will now be in 250 ml

With this, we can calculate the final concentration (in M, or moles/Lt):

250ml=(X/5000) moles KNO₃

1000ml=2/250×X M KNO₃

So, once you know the original concentration of KNO₃ solution, you should just multiply this number by (2/250) to get final concentration of 250 ml solution obtained by multiple dilutions