Hydrogen is placed inside a container and kept at a constant pressure. The graph shows the estimated volume y, in...

1. TRANSLATE the problem information

The question asks: "What is the estimated volume, in liters, of the hydrogen when its temperature is 500 kelvins?"

Let's break down what this means:

• Given: Temperature = 500 kelvins
• Find: Volume in liters
• From the graph:
  • X-axis = Temperature (kelvins)
  • Y-axis = Volume (liters)

This translates to: Find the y-value when \(\mathrm{x = 500}\)

2. VISUALIZE by reading the graph

To find the volume at 500 kelvins:

1. Locate 500 on the x-axis (Temperature axis)
   • Look at the bottom horizontal axis
   • Find the mark at 500 kelvins (it's in the middle of the scale)
2. Trace vertically upward from \(\mathrm{x = 500}\) until you hit the line
3. From that point on the line, trace horizontally left to the y-axis
4. Read the value on the y-axis
   • The y-coordinate is 7

Therefore, when the temperature is 500 kelvins, the volume is 7 liters.

Answer: C. 7

Why Students Usually Falter on This Problem

Most Common Error Path:

TRANSLATE error - Confusing the task with finding a rate or ratio:

Some students see the numbers 7 and 500 on the graph and think they need to calculate a relationship between them, such as the slope or rate of change. They might compute:

• \(\mathrm{7 ÷ 500 = \frac{7}{500}}\)

This is incorrect because the question asks for a specific value (the volume at 500 kelvins), not a rate of change. The answer should be a single number read directly from the graph, not a calculated ratio.

This may lead them to select Choice B (\(\mathrm{\frac{7}{500}}\))

Second Most Common Error:

TRANSLATE error - Inverting the variables:

Some students might confuse which axis represents which variable, or they might invert the relationship, thinking they need to find x when y = 7, then express it as a fraction: \(\mathrm{\frac{500}{7}}\).

Alternatively, they might mistakenly think the answer should be expressed as "kelvins per liter" rather than just "liters," leading them to compute \(\mathrm{\frac{500}{7}}\).

This may lead them to select Choice D (\(\mathrm{\frac{500}{7}}\))

The Bottom Line:

This problem tests your ability to TRANSLATE a word question into a graph-reading task. The key is recognizing that "What is the volume when temperature is 500?" simply means "Find the y-value at \(\mathrm{x = 500}\)"—no calculations needed, just careful graph reading. Don't overthink it by looking for ratios or slopes; the answer is a direct reading from the graph.