A gas sample occupies 4.2 Liters at a pressure of 101 kPa. What volume will the will it occupy if the pressure is increased to 235 kPa?
P V = n R T
n the same number of mols
R the same
I guess we assume T does not change
so
P2 V2 = P1 V1
To solve this problem, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, assuming that the temperature remains constant.
Boyle's Law equation is:
P₁V₁ = P₂V₂
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Let's substitute the given values into the equation:
P₁ = 101 kPa
V₁ = 4.2 Liters
P₂ = 235 kPa
V₂ = ?
101 kPa * 4.2 L = 235 kPa * V₂
Now, let's solve for V₂:
V₂ = (101 kPa * 4.2 L) / 235 kPa
V₂ = (424.2 kPa * L) / 235 kPa
V₂ ≈ 1.806 L
Therefore, the gas sample will occupy approximately 1.806 Liters when the pressure is increased to 235 kPa.
To determine the volume the gas sample will occupy when the pressure is increased, we can use the combined gas law equation, which relates the initial and final states of a gas sample:
\(P_1 \cdot V_1 / T_1 = P_2 \cdot V_2 / T_2\)
Where:
\(P_1\) is the initial pressure (101 kPa),
\(V_1\) is the initial volume (4.2 L),
\(P_2\) is the final pressure (235 kPa), and
\(V_2\) is the final volume (which we need to find).
However, it is important to note that the combined gas law equation assumes that the temperature remains constant. Therefore, we can assume the temperature (T1) and (T2) are constant, cancel them out from the equation, and rewrite the equation as:
\(P_1 \cdot V_1 = P_2 \cdot V_2\)
Now, we can substitute the known values into the equation and solve for \(V_2\) (the final volume).
\(P_1 \cdot V_1 = P_2 \cdot V_2\)
\(101 \text{ kPa} \cdot 4.2 \text{ L} = 235 \text{ kPa} \cdot V_2\)
Simplifying the equation:
\(426.2 = 235 \cdot V_2\)
Now, solve for \(V_2\) by dividing both sides of the equation by 235:
\(V_2 = \frac{426.2}{235}\)
\(V_2 \approx 1.814\, \text{L}\)
Therefore, when the pressure is increased to 235 kPa, the gas sample will occupy approximately 1.814 Liters.