Question

*85. interpret graphs the mass of the elements iron and oxygen in four samples of a rust-colored substance was measured in grams (g). the amount of iron and oxygen in each sample is shown on the graph.

mass of elements in samples
graph with x-axis: mass of oxygen (g), y-axis: mass of iron (g), data points at (2, 5), (4, ~8), (6, 15), (8, ~18)

a. do you think all four samples are the same compound? explain.

b. another sample of similar material was found to contain 9.9 grams of iron and 3.4 grams of oxygen. is this sample the same substance as the other four samples? explain.

Explanation:

Part (a)

Step1: Recall Law of Definite Proportions

A compound has elements in a fixed mass ratio. So, check the iron - oxygen mass ratio for each sample.

Step2: Calculate ratio for given points

• For the first point (oxygen = 2g, iron = 5g): Ratio \(=\frac{5}{2}=2.5\)
• Second point (oxygen = 4g, iron = 8g? Wait, no, looking at the graph: Wait, first point (2,5), second (4,8? No, wait the line: Let's take the points. Let's see, when oxygen is 2g, iron is 5g. When oxygen is 4g, iron is 8? Wait no, maybe the slope. Wait, the line passes through (2,5), (4,8)? No, wait 5/2 = 2.5, 8/4 = 2, no, wait maybe I misread. Wait, the graph: x - axis oxygen (g), y - axis iron (g). The points: (2,5), (4,8)? No, 5/2 = 2.5, 8/4 = 2? No, that can't be. Wait, maybe (2,5), (4,8) is wrong. Wait, let's recalculate. Wait, 5g iron when oxygen is 2g: ratio 5/2 = 2.5. Then next point: when oxygen is 4g, iron is 8? No, 8/4 = 2, that's different. Wait, no, maybe the points are (2,5), (4,8) is incorrect. Wait, maybe the line is linear, so the ratio of iron to oxygen should be constant. Let's check the slope. Slope \(m=\frac{\Delta y}{\Delta x}=\frac{5 - 0}{2 - 0}=2.5\) (assuming when oxygen is 0, iron is 0, but the first point is (2,5)). So the equation is \(y = 2.5x\), where \(y\) is iron mass, \(x\) is oxygen mass. So for each sample, the ratio of iron to oxygen is \(2.5\) (or \(5:2\)). So all samples have the same mass ratio of iron to oxygen. By the Law of Definite Proportions, they are the same compound.

Step1: Calculate the ratio for the new sample

The new sample has 9.9 g iron and 3.4 g oxygen. Calculate the ratio \(\frac{\text{mass of iron}}{\text{mass of oxygen}}=\frac{9.9}{3.4}\approx2.91\)

Step2: Compare with the ratio from part (a)

From part (a), the ratio of iron to oxygen for the four samples is \(2.5\) (or \(\frac{5}{2}\)). Since \(2.91
eq2.5\), the mass ratio of iron to oxygen is different. By the Law of Definite Proportions, a compound has a fixed mass ratio of elements. So this sample is not the same substance.

Answer:

Yes, all four samples are the same compound. This is because the mass ratio of iron to oxygen is constant for each sample (e.g., for the first sample with 2 g oxygen and 5 g iron, the ratio is \(\frac{5}{2}=2.5\); other samples will have the same ratio as the graph is a straight line, indicating a fixed proportion of elements, consistent with the Law of Definite Proportions for compounds.

Part (b)