Question

A 256 mL sample of HCl gas is in a flask where it exerts a force (pressure) of 67.5 mmHg. What is the pressure of the gas if it were transferred to a 135 mL flask

Answer 1

The pressure in the new flask would be
`128\; \rm mmHg` if the
`\rm HCl` here acts like an ideal gas.

Step-by-step explanation:

Assume that the
`\rm HCl` sample here acts like an ideal gas. By Boyle's Law, the pressure
`P` of the gas should be inversely proportional to its volume
`V`.

For example, let the initial volume and pressure of the sample be
`V_1` and
`P_1`. The new volume
`V_2` and pressure
`P_2` of this sample shall satisfy the equation:
`P_1 \cdot V_1 =P_2 \cdot V_2`.

In this question,

• The initial volume of the gas is
  `V_1= 256\; \rm mL`.
• The initial pressure of the gas is
  `P_1 = 67.5\; \rm mmHg`.
• The new volume of the gas is
  `V_2 = 135\; \rm mL`.

The goal is to find the new pressure of this gas,
`P_2`.

Assume that this sample is indeed an ideal gas. Then the equation
`P_1 \cdot V_1 =P_2 \cdot V_2` should still hold. Rearrange the equation to separate the unknown,
`P_2`. Note: make sure that the units for
`V_1` and
`V_2` are the same before evaluating. That way, the unit of

`\begin{aligned} & P_2\\ &= (P_1 \cdot V_1)/(V_2) \\ &= (256\; \rm mL * 67.5\; \rm mmHg)/(135\; \rm mL) \\ & \approx 128\; \rm mmHg\end{aligned}`.