Algebra with science

Question

The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is

600

cubic centimeters when the pressure is

250

millimeters of mercury​ (mm Hg), find the volume when the pressure is

300

mm Hg.

Answer 1

The first sentence of this question is equivalent to the mathematical statement: PV = Constant.

Expressing this relationship for two different thermodynamic states: P₁V₁ = P₂V₂. This equation can

be solved for V₂ = V₁ [P₁/P₂].

Substituting values: V₂ = 600 cm³ [250/300] = 500 cm³.

Answer 2

Hi,

For this situation, we are using a specific part of the Ideal gas law (PV = nRT) known as Boyle's Law. Pressure and Volume are inversely proportional. In other words, as one increases, the other decreases. Since our pressure is increasing, then our volume must be decreasing.

We can set it up as a simple equation, P_i·V_i = P_f·V_f

The subscripts i and f represent the initial and final.

P_i = 250 mm Hg

V_i = 600 cm³

P_f = 300 mm Hg

V_f = ?

We can now plug in our known values and solve for V_f. 250•600/300 = V_f

The volume has decreased from 600 to 500 cm³. This agrees with our statement above that volume must be decreasing.