Ideal Gas Molecules
5 marks · EasyA scientist traps a fixed mass of gas in a syringe sealed with a cap. She gently heats the syringe by placing it in warm water while making sure the plunger does not move. The initial temperature of the gas is 25°C and its pressure is 105 kPa. After heating, the gas temperature reaches 45°C. Assume the volume of the gas does not change.
State which gas law links the pressure and temperature of a fixed volume of gas.
Calculate the new pressure of the gas when it has reached 45°C. Give your answer to two significant figures.
Explain, in terms of the motion of particles, why the pressure increases when the gas is heated.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Pressure law (or the pressure-temperature law)
(b) 112 kPa · must show T1 = 25°C + 273 = 298 K, T2 = 45°C + 273 = 318 K, p1/T1 = p2/T2, p2 = p1 × T2/T1
(c) Particles move faster and collide with the walls more often and with greater force, so the pressure increases. · must show increased speed/kinetic energy, more frequent/harder collisions
Common mistakes: Not converting Celsius to Kelvin; Using the wrong equation
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Marking points
B1 (a) · 1 mark · Correctly states pressure-temperature law or pressure law.
M1 (b) · 1 mark · Converts temperatures to Kelvin (25°C + 273 and 45°C + 273), states p1/T1 = p2/T2 and rearranges correctly.
M2 (b) · 1 mark · Substitutes values correctly (105/298 = p2/318). (follow-through)
A1 (b) · 1 mark · Arrives at final answer: 112 kPa to 2 significant figures. (follow-through)
B2 (c) · 1 mark · Explains increased pressure in terms of faster, harder or more frequent collisions due to increased speed/kinetic energy.
Worked solution
a) The law is called the pressure law (or the pressure-temperature law).
b) First, convert temperatures to Kelvin:
Use the pressure law:
c) When the gas is heated, its particles move faster, so they hit the container walls more often and with greater force. This increases the pressure.