A student investigates the corrosion of iron in various acidic solutions. The student hypo… — ACT

A student investigates the corrosion of iron in various acidic solutions. The student hypothesizes that the rate of corrosion, measured by the mass loss of an iron nail after $48\text{ hours}$ , increases linearly as the pH of the solution decreases from $7.0$ to $2.0$ . The student places identical iron nails in solutions of varying pH and records the mass loss in the table below:

pH of solution	Mass loss of iron nail (\text{mg})
$7.0$	$0.8$
$6.0$	$1.6$
$5.0$	$2.4$
$4.0$	$3.2$
$3.0$	$3.8$
$2.0$	$4.0$

Based on these results, which of the following statements best describes how the student should modify their hypothesis?

The rate of corrosion increases linearly as pH decreases from $7.0$ to $4.0$ , but the rate of increase begins to level off at a pH below $4.0$ .Answer
B
The rate of corrosion increases by a constant value of $0.8\text{ mg}$ for every $1.0\text{ unit}$ decrease in pH across the entire range of $7.0$ to $2.0$ .
C
The rate of corrosion decreases as the pH of the solution decreases from $7.0$ to $4.0$ , then increases at lower pH values.
D
The rate of corrosion remains constant at all pH values below $5.0$ .

Answer

The rate of corrosion increases linearly as pH decreases from 7.0 to 4.0, but the rate of increase begins to level off at a pH below 4.0.

The correct option correctly identifies that from pH 7.0 to 4.0, the mass loss increases by exactly 0.8 mg for each 1.0-unit decrease in pH, showing a linear relationship. Below pH 4.0, the mass loss increases by 0.6 mg (from pH 4.0 to 3.0) and then by 0.2 mg (from pH 3.0 to 2.0), which shows that the rate of increase is leveling off.

Step-by-Step Solution

Analyze the student's initial hypothesis and the trend in the data.

The hypothesis predicts a constant, linear increase in mass loss (corrosion rate) as pH decreases from

7.0

2.0

. The data shows that as pH decreases from

7.0

4.0

, the mass loss increases by a constant

0.8\text{ mg}

per

1.0

pH unit (

0.8 \rightarrow 1.6 \rightarrow 2.4 \rightarrow 3.2

Establishing the baseline relationship helps identify where the data aligns with or deviates from the linear prediction.

Examine the data for pH values below

4.0

to determine if the linear trend continues.

From pH

4.0

3.0

, the mass loss increases by

0.6\text{ mg}

(

3.2 \rightarrow 3.8\text{ mg}

). From pH

3.0

2.0

, the mass loss increases by only

0.2\text{ mg}

(

3.8 \rightarrow 4.0\text{ mg}

Calculating the rate of change at lower pH values reveals whether the relationship remains strictly linear.

Formulate a modified hypothesis that accurately describes the entire dataset.

The rate of corrosion increases linearly as pH decreases from

7.0

4.0

, but the rate of increase begins to level off (increase by smaller amounts) at pH values below

4.0

A modified hypothesis must reflect both the initial linear range and the subsequent non-linear leveling off shown in the data.

Key Concept

Formulating and Modifying Hypotheses

Estimated Time:1m 30s

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