A student investigates Boyle's law by trapping air in a syringe and recording pressure at different volumes. Table 34.1 shows her results. The temperature r...
Question 1 Report
A student investigates Boyle's law by trapping air in a syringe and recording pressure at different volumes. Table 34.1 shows her results. The temperature remains constant at 22 °C throughout the experiment. The syringe plunger moves freely without friction and no air leaks. Some values in the table are missing. The student notices that the product of pressure and volume should be constant for all readings if Boyle's law holds. She also wants to predict the volume when the pressure is 250 kPa. The air behaves as an ideal gas at this temperature and pressure range.
Table 34.1
| p / kPa | V / cm³ | pV / kPa cm³ |
|---|---|---|
| 100 | 60 | ............ |
| 120 | 50 | ............ |
| 150 | 40 | 6000 |
| 200 | 30 | 6000 |
(a) Complete the missing values of pV in the table. [2]
(b) Sketch a graph of p against V using the data in the table. [2]
(c) State the relationship demonstrated by the constant value of pV. [1]
(d) Calculate the volume when the pressure is 250 kPa. [3]
Answer Details
(a) Completing the missing pV values [2]
| p / kPa | V / cm3 | pV / kPa cm3 |
|---|---|---|
| 100 | 60 | 6000 [1] |
| 120 | 50 | 6000 [1] |
| 150 | 40 | 6000 |
| 200 | 30 | 6000 |
For the first row: pV = 100 × 60 = 6000 kPa cm3. For the second row: pV = 120 × 50 = 6000 kPa cm3. All four rows give the same product, confirming that Boyle's law holds.
(b) Graph of p against V [2]
The graph is a smooth hyperbolic curve. Axes are labelled with p / kPa on the y-axis and V / cm3 on the x-axis. [1] The curve passes through all four data points, decreasing steeply at small volumes and levelling off at larger volumes, which is the characteristic shape of an inverse proportionality. [1]
(c) Relationship demonstrated by the constant pV value [1]
Pressure is inversely proportional to volume at constant temperature. [1] This is Boyle's law. The constant product pV = 6000 kPa cm3 confirms p ∝ 1/V: as one variable doubles, the other halves.
(d) Calculating volume at 250 kPa [3]
Since pV = constant = 6000 kPa cm3 [1]
V = 6000 / 250 [1]
V = 24 cm3 [1]
At 250 kPa, the gas is compressed to only 24 cm3, which is consistent with the trend: as pressure increases beyond the tabulated values, volume continues to decrease.
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