Question

the initial temperature of a 250 ml of a gas is 45 degrees Celsius with a pressure of of 689 mm Hg. what will be the new pressure if the volume is lowered to 150 ml at a temperature of 95 degrees Celsius?

Answer 1

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, although it has several limitations. The ideal gas law is often introduced in its common form: It's possible to solve this task by using next formula:

$$\mathrm{PV} = \mathrm{nRT}, \text{ where:}$$

P – Pressure

V – Volume

T – Temperature

R – Gas constant

n – Amount

In this task n and R are constants, but P, V and T are different, so

$$\mathrm{nR} = \mathrm{P_1V_1 / T_1}, \text{ and}$$ $$\mathrm{nR} = \mathrm{P_2V_2 / T_2}, \text{ so}$$ $$(\mathrm{P_1V_1}) / \mathrm{T_1} = (\mathrm{P_2V_2}) / \mathrm{T_2}, \text{ where:}$$

The new pressure is $\mathrm{P_2}$, and it is:

$$\mathrm{P_2} = (\mathrm{P_1V_1} \cdot \mathrm{T_2}) / \mathrm{T_1V_2}$$ $$\mathrm{P_2} = 689 \cdot 250 \cdot (273 + 45) / (273 + 95) \cdot 150 = 992 \text{ mm Hg}$$

The new pressure is $992 \text{ mm Hg}$.