Assuming that the temperature and quantity of a gas sample remain constant, what will be the final pressure of 1.6 L sample of gas originally at 330K and 4.84 atm, when the volume is reduced to 840 mL?
To calculate the final pressure of the gas sample after the volume is reduced, we can use the Boyle's Law equation, which states that the pressure and volume of a gas are inversely proportional when temperature and quantity are constant.
First, let's convert the initial and final volumes to the same unit. Since the initial volume is given in liters (L) and the final volume is given in milliliters (mL), we need to convert mL to L by dividing by 1000:
Initial Volume: 1.6 L
Final Volume: 840 mL ÷ 1000 = 0.84 L
According to Boyle's Law, the product of the initial pressure and volume should equal the product of the final pressure and volume. Therefore:
(P1 x V1) = (P2 x V2)
Substituting the given values:
(4.84 atm x 1.6 L) = (P2 x 0.84 L)
To solve for P2 (final pressure), rearrange the equation:
P2 = (4.84 x 1.6) / 0.84
Final Pressure (P2) = 9.2848 atm (rounded to four decimal places)
Therefore, the final pressure of the gas sample, when the volume is reduced to 840 mL, will be approximately 9.2848 atm.
To find the final pressure of the gas sample, we can use Boyle's Law, which states that the pressure of a given amount of gas is inversely proportional to its volume, as long as the temperature and quantity of the gas remain constant.
Boyle's Law equation: P1 * V1 = P2 * V2
Where:
P1 = Initial pressure of the gas
V1 = Initial volume of the gas
P2 = Final pressure of the gas (what we want to find)
V2 = Final volume of the gas
Given information:
P1 = 4.84 atm
V1 = 1.6 L
V2 = 840 mL
Now, we need to convert the volume from milliliters (mL) to liters (L) because Boyle's Law equation requires both values to be in the same unit.
1 L = 1000 mL
Substituting the values into Boyle's Law equation:
P1 * V1 = P2 * V2
4.84 atm * 1.6 L = P2 * (840 mL / 1000)
7.74 atm = P2 * 0.84
To isolate P2 (final pressure), divide both sides of the equation by 0.84:
7.74 atm / 0.84 = P2
P2 = 9.21 atm
Therefore, the final pressure of the gas sample, when the volume is reduced to 840 mL, will be approximately 9.21 atm.