Question

The reduced form of nicotinamide adenine dinucleotide (NADH) is an important and highly fluorescent coenzyme. It has an absorption maximum of 340 nm and an emission maximum at 465 nm. Standard solutions of NADH gave the following fluorescence intensities:

(a) Construct a spreadsheet and use it to draw a calibration curve for NADH.

*(b) Find the least-squares slope and intercept for the plot in (a).

(c) Calculate the standard deviation of the slope and the standard deviation about regression for the curve.

*(d) An unknown exhibits a relative fluorescence intensity of 12.16. Use the spreadsheet to calculate the

concentration of NADH.

*(e) Calculate the relative standard deviation for the result in part (d).

*(f) Calculate the relative standard deviation for the result in part (d) if a result of 7.95 was the mean of three measurements.

Short answer

a)

b) Slope = 22.34643

Intercept = 0.000357

c)$$\begin{gathered} s_m=0.269613 \\ {s}_r=0.174729 \end{gathered}$$

d) $0.544\mathrm{\mu mol}/\mathrm{L}$

e) RSD = 1.57 %

f) RSD= 2.39 %

Step-by-step solution

Part (a) Step 1: Given Information

The calibration curve should be constructed in a spread sheet.

Part (a) Step 2: Explanation

Relative intensity is the dependent variable and concentration of NADH is the independent variable. A plot of relative intensity versus concentration of NADH should be drawn.

Part (b) Step 1: Given Information

The least square slope and the intercept for the plot in (a) should be determined.

Part (b) Step 2: Explanation

According to the least squares analysis done in spreadsheet

Slope = 22.34643

Intercept = 0.000357

Part (c) Step 1: Given Information

The standard deviation of the slope and the standard deviation about regression for the curve should be determined.

Part (c) Step 2: Explanation

According to the least squares analysis done in spread sheet

$$\begin{gathered} s_m=0.269613 \\ {s}_r=0.174729 \end{gathered}$$

Where,

Standard deviation about regression, $s_r=\sqrt{\frac{S_{xy}-m^2{S}_{xx}}{N-2}}$

N – number of points used.

The standard deviation of the slope, $s_m=\sqrt{\frac{{s_r}^2}{S_{xx}}}$

The standard deviation of the intercept, $s_b=s_r\sqrt{\frac{\sum _{{x_i}^2}}{N\sum _{{x_i}^2}-{\left(\sum _{x_i}\right)}^2}}$

Part (d) Step 1: Given Information

The concentration of unknown NADH sample should be calculated using the spreadsheet.

Part (d) Step 2: Explanation

Equation for the least square line of the graph

$$\begin{gathered} y=22.34643x+0.000357 \\ 12.16=22.34643x+0.000357 \\ 12.159643=22.34643x \\ x=0.544\mathrm{\mu mol}/\mathrm{L} \end{gathered}$$

Part (e) Step 1: Given Information

The relative standard deviation for the result in part (d) should be calculated.

Part (e) Step 2: Explanation

$$\begin{gathered} s_c=\frac{0.174729}{22.34643}\sqrt{\frac{1}{1}+\frac{1}{6}+\frac{{(12.16-10.05625)}^2}{{(22.34643)}^2\times 0.42}} \\ {s}_c=8.5216\times {10}^{-3} \\ RSD=\frac{8.5216\times {10}^{-3}}{0.544}\times 100 \\ RSD=1.57\% \end{gathered}$$

Part (f) Step 1: Given Information

The relative standard deviation for the result in part (d) should be calculated if a result of 7.95 was the mean of three measurements.

Part (f) Step 2: Explanation

$$\begin{gathered} y=22.34643x+0.000357 \\ 7.95=22.34643x+0.000357 \\ 7.949643=22.34643x \\ x=0.356\mathrm{\mu mol}/\mathrm{L} \end{gathered}$$

$$\begin{gathered} s_c=\frac{0.174729}{22.34643}\sqrt{\frac{1}{3}+\frac{1}{6}+\frac{{(7.95-10.05625)}^2}{{(22.34643)}^2\times 0.42}} \\ {s}_c=8.5218\times {10}^{-3} \\ RSD=\frac{8.5218\times {10}^{-3}}{0.356}\times 100 \\ RSD=2.39\% \end{gathered}$$