Oxygen gas inside a 1.5 L gas tank has a pressure of 0.95 atm. Provided that the temperature remains constant, how much pressure is needed to reduce its volume by 1/2?
Using Boyle's law formula
Answers
New pressure will be - 1.9 atm.
Boyle's law states that "pressure of a given quantity of gas is inversely proportional to its volume at a constant temperature."
The equation representing Boyle's law is P1V1 = P2V2
P1 and P2 represent initial and final pressure and V1 and V2 represent the initial and final volume.
Initial pressure given in the question is 0.95 atm.
The initial volume is 1.5 l and the final volume is 1/2 of its value, thus 0.75l.
Keeping values in the formula,
0.95*1.5 = P2*0.75
P2 = 1.9 atm
Thus, new pressure will be 1.9 atm.
Answer:
The pressure needed to reduce the volume by 1/2 is 1.9 atm.
Explanation:
This problem is an application of the Boyle's Law. Boyle's law is a relationship between pressure and volume of gases. It states that an inverse relationship between the pressure and volume of a gas exists when the temperature is constant.
The equation for this law is as follows:
P₁V₁ = P₂V₂
where P₁ is the initial pressure, P₂ is the final pressure, V₁ is the initial volume, and V₂ is the final volume.
We are given with the values of P₁ and V₁, then the problem said that V₂ is reduced to 1/2 of its original value.
Solving first for V₂ we have
V₂ = V₁ - (1/2)(V₁)
V₂ = 1.5 L - (1/2)(1.5 L)
V₂ = 0.75 L
Using the value of V₂ from the previous step, we now solve for P₂. Our equation will be
P₂ =
Substituting the values:
P₂ =
P₂ = 1.9 atm
Hence the final pressure of oxygen gas needed to reduce its volume to half of its original volume is 1.9 atm.
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