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The concentration of \(\mathrm{Na}\) in plant materials are determined by flame atomic emission. The material to be analyzed is prepared by grinding, homogenizing, and drying at \(103^{\circ} \mathrm{C}\). A sample of approximately \(4 \mathrm{~g}\) is transferred to a quartz crucible and heated on a hot plate to char the organic material. The sample is heated in a muffle furnace at \(550^{\circ} \mathrm{C}\) for several hours. After cooling to room temperature the residue is dissolved by adding \(2 \mathrm{~mL}\) of \(1: 1 \mathrm{HNO}_{3}\) and evaporated to dryness. The residue is redissolved in \(10 \mathrm{~mL}\) of \(1: 9 \mathrm{HNO}_{3},\) filtered and diluted to \(50 \mathrm{~mL}\) in a volumetric flask. The following data are obtained during a typical analysis for the concentration of \(\mathrm{Na}\) in a \(4.0264-\mathrm{g}\) sample of oat bran. $$ \begin{array}{lcc} {\text { sample }} & \mathrm{mg} \mathrm{Na} / \mathrm{L} & \text { emission (arbitrary units) } \\ \hline \text { blank } & 0.00 & 0.0 \\ \text { standard 1 } & 2.00 & 90.3 \\ \text { standard } 2 & 4.00 & 181 \\ \text { standard } 3 & 6.00 & 272 \\ \text { standard } 4 & 8.00 & 363 \\ \text { standard } 5 & 10.00 & 448 \\ \text { sample } & & 238 \end{array} $$ Report the concentration of sodium in the sample of oat bran as \mug Na/g sample.

Step by step solution

01

Plot a Calibration Curve and Determine Line Equation

First, we plot a calibration curve using the given standard data: | mg Na/L | Emission ||---------|----------|| 0.00 | 0.0 || 2.00 | 90.3 || 4.00 | 181 || 6.00 | 272 || 8.00 | 363 || 10.00 | 448 |A linear regression on these points yields the equation of the line: \[y = 44.8x\]where **y** is the emission (arbitrary units) and **x** is the concentration in mg Na/L.

02

Determine Sodium Concentration in Sample Solution

Now that we have the calibration curve equation, we'll use it to find the concentration of Na in the sample. The sample emission is 238 arbitrary units.Using the line equation: \[238 = 44.8x \]Solve for **x**:\[x = \frac{238}{44.8} \approx 5.31 \text{ mg Na/L}\]

03

Convert Sodium Concentration to µg Na/g Sample

The concentration obtained from the emission is in mg Na/L for the sample solution. We need to convert it to µg Na/g sample. The sample of oat bran is diluted to a volume of 50 ml = 0.050 L. Therefore, the total mass of Na in the solution is:\[\text{Total mass} = 5.31 \text{ mg/L} \times 0.050 \text{ L} = 0.2655 \text{ mg}\]Convert this mass into micrograms (µg): \[0.2655 \text{ mg} = 265.5 \text{ µg} \]Since the sample mass is 4.0264 g, the concentration in the sample is:\[\frac{265.5 \text{ µg}}{4.0264 \text{ g}} \approx 65.9 \text{ µg Na/g sample}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calibration Curve

In Flame Atomic Emission Spectroscopy, the calibration curve is a crucial tool used to determine the concentration of an element in a sample. This curve is created by plotting known concentrations (standards) of an element against their corresponding emission values. In our case:

- We have data points with known mg Na/L and their respective emission values in arbitrary units.
- By plotting these points on a graph, a linear relationship can be established. This is often represented by a straight line.
- The equation of this line is critical as it allows us to find unknown concentrations by inputting the sample's emission value.

The calibration curve obtained was a linear equation: \[ y = 44.8x \]where **y** is the emission value and **x** is the concentration in mg Na/L. This equation helps to translate emission values directly into concentrations.

Sodium Concentration

Once the calibration curve is established, determining the sodium concentration in the sample becomes straightforward. For the oat bran sample, its emission value is given as 238 arbitrary units. Using the line equation from the calibration curve:\[ 238 = 44.8x \]we solve for **x** to find the concentration of sodium in the sample solution.

Solving gives us:\[ x = \frac{238}{44.8} \approx 5.31 \text{ mg Na/L} \]

This concentration represents how much sodium is present in each liter of the prepared sample solution. However, to understand the amount of sodium per unit of oat bran (the actual sample), further conversion is necessary.

Sample Preparation

Sample preparation is an often overlooked but fundamental step in obtaining accurate results in Flame Atomic Emission Spectroscopy. In our exercise, the oat bran is thoroughly prepped before analysis:

- The plant material is first ground, homogenized, and then dried to ensure consistency.
- A sample is charred and ashed to decompose organic material, leaving behind an inorganic residue.
- This residue needs to be dissolved and diluted. It's initially mixed with nitric acid (HNO₃) and then converted to a solution with precise volume.

This meticulous preparation is crucial to reduce errors and ensure that the sodium measured is accurately representative of the sample. It allows us to relate the concentration of sodium in the solution back to the actual sample, leading to the final concentration expressed as micrograms \( \text{µg Na/g sample} \). Proper preparation ensures reproducibility and accuracy.