A gas occupies a volume of 458 mL at a
pressure of 1.01 kPa and a temperature of
295 K. When the pressure is changed, the
volume becomes 477 mL. If there has been
no change in temperature, what is the new
pressure?
Sorry its 0.969 kpa
1.06 kpa
teacher
Well, well, well, looks like we have ourselves a gas who can't handle pressure. Don't worry, I'll help you out. Now, let's dive into the world of gases.
We know that the initial volume (Vi) of our gas is 458 mL, the initial pressure (Pi) is 1.01 kPa, and the final volume (Vf) is 477 mL. Since there's no change in temperature, we can use the good old Boyle's Law.
According to Boyle's Law, the product of the initial pressure and volume (Pi × Vi) is equal to the product of the final pressure and volume (Pf × Vf). Mathematically, we can write it as:
(Pi × Vi) = (Pf × Vf)
Plugging in the values we know:
(1.01 kPa × 458 mL) = (Pf × 477 mL)
Now, let's solve for Pf, which is the new pressure our gas will be facing:
Pf = (1.01 kPa × 458 mL) / 477 mL
Calculating...
Pf ≈ 0.971 kPa
So, the new pressure for our gas is approximately 0.971 kPa. Just remember, even gases need to learn how to handle pressure in life. Stay strong, little gas!
To find the new pressure, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Mathematically, it can be represented as:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure (what we want to find)
V2 = final volume
Given:
P1 = 1.01 kPa
V1 = 458 mL
V2 = 477 mL
Let's plug in the given values into the equation and solve for P2:
P1 * V1 = P2 * V2
1.01 kPa * 458 mL = P2 * 477 mL
Now, let's cancel out the units:
(1.01 kPa * 458 mL) / 477 mL = P2
Calculating this expression gives us the new pressure, P2.
P1V1 = P2V2
Substitute and solve for the one unknown. Post your work if you need additional assistance.