A blood serum sample containing Na+ gave an emission signal of 4.27 mV. A small volume of concentrated standard Na+ was then added to increase the Na+ concentration by 0.102 M, without significantly diluting the sample. This "spiked" serum sample gave a signal of 8.09 mV. Find the original concentration of Na+ in the serum.
Answer is suppose to be 0.117 but I'm just not getting those numbers.
0.102M is responsible for 8.09-4.27 = 3.82 mv.
Then 0.102 x (4.27/3.82) = 0.114M
To find the original concentration of Na+ in the serum, we can use the concept of dilution.
Let's break down the information provided:
Original signal (before adding standard Na+): 4.27 mV
Signal after adding standard Na+: 8.09 mV
Increase in Na+ concentration after adding standard Na+: 0.102 M
To solve the problem, we need to understand the relationship between the change in signal and the change in concentration.
The signal produced is directly proportional to the concentration of Na+. This implies that if the concentration of Na+ doubles, the signal will double as well.
Let's calculate the change in signal:
Change in Signal = Signal after adding standard Na+ - Original signal
Change in Signal = 8.09 mV - 4.27 mV
Change in Signal = 3.82 mV
Now we can calculate the change in concentration:
Change in Concentration = Increase in Na+ concentration after adding standard Na+
Change in Concentration = 0.102 M
Since the change in signal is proportional to the change in concentration, we can set up a ratio:
Change in Signal / Change in Concentration = Original signal / Original concentration
Plugging in the values we have:
3.82 mV / 0.102 M = 4.27 mV / Original concentration
Now we can solve for the original concentration:
Original concentration = (4.27 mV * 0.102 M) / 3.82 mV
Original concentration ≈ 0.114 M
Therefore, the original concentration of Na+ in the serum is approximately 0.114 M, not 0.117 M as mentioned in the answer. Double-check the calculations and ensure that you've used the correct provided values to reach the correct answer of 0.114 M.