a) Answer:
= 225 mL
Explanation:
Using Boyle's law of gases;
The volume of a fixed mass of a gas is inversely proportional to its pressure at constant temperature.
Therefore;
P1V1 = P2V2
in this case; let the initial pressure be P;
Therefore; V1 = 450 mL, P1 = P, V2 = ? and P2 = 2P
Thus;
V2 = P1V1/P2
= (P×450)/ (2P)
= 225 mL
Therefore, the new volume will be 225 mL
b) Answer;
=1800 mL
Explanation;
Let the initial pressure be P;
Therefore; V1 = 450 mL, P1 = P, V2 = ? and P2 = 1/4P
Thus;
V2 = P1V1/P2
= (P×450)/(0.25P)
= 1800 mL
Thus, when the pressure is reduced to one-fourth of its original, the new volume will be 1800 mL.
Given that the initial volume of the gas is 450 mL, the new volume of the gas obtained based on the given data are:
A. The new volume of the gas when the pressure is doubled is 225 mL
B. The new volume of the gas when the pressure is reduced to one-fourth of its original value is 1800 mL
P₁V₁ / T₁ = P₂V₂ / T₂
Since the temperature is constant, we have:
P₁V₁ = P₂V₂
P × 450 = 2P × V₂
Divide both side by 2P
V₂ = (P × 450) / 2P
V₂ = 450 / 2
V₂ = 225 mL
P₁V₁ / T₁ = P₂V₂ / T₂
Since the temperature is constant, we have:
P₁V₁ = P₂V₂
P × 450 = ¼P × V₂
450P = PV₂ / 4
Cross multiply
450P × 4 = PV₂
Divide both side by P
V₂ = (450P × 4) / P
V₂ = 450 × 4
V₂ = 1800 mL
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