What is the original concentration of Li^+ in the serum?

Question

The lithium concentration in serum taken from a patient being treated with lithium for manic-depressive illness was analyzed using flame emission spectroscopy. A sample of the serum gave a reading of  309 units for the intensity of the 671 nm red emission line. Then, 1.00 mL of a 10.8 mM lithium standard was added to 9.00 mL of serum. This spiked serum gave an intensity reading of  623 units at the 671 nm emission line. What is the original concentration of  Li^+ in the serum?

Answer 1

1.00 ml (10.8 mM) = (10 ml)(x mM) and x = 1.08 mM Li⁺ in the spiked sample

Unknown = 309 units

Unknown + 1.08 mM Li⁺ = 623 units

1.08 mM Li⁺ = 623 - 309 = 314 units

Assuming linearity, we can estimate the [Li⁺] in the unknown.

314 U/309 U = 1.08 mM/x mM

x = 1.06 mM Li⁺