a sample of argon gas at standard pressure occupies 100ml. At constant temperature, what volume does the gas occupy if the pressure increases to 800 mm hg? show working please.
since PV = kT
Since T is constant, PV is constant
So, you want to find V such that
800V = 760*100
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Mathematically, this relationship can be expressed as P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, we are given P1 = standard pressure = 1 atm, V1 = 100 ml, and P2 = 800 mmHg. To use Boyle's Law, we need to convert all the pressures to the same units.
Step 1: Convert the initial pressure from 1 atm to mmHg.
1 atm = 760 mmHg (standard conversion factor)
So, P1 = 1 atm * 760 mmHg/atm = 760 mmHg
Step 2: Apply Boyle's Law to find V2.
P1 * V1 = P2 * V2
760 mmHg * 100 ml = 800 mmHg * V2
Simplifying the equation,
V2 = (760 mmHg * 100 ml) / 800 mmHg
Step 3: Solve for V2.
V2 = (76000 ml * mmHg) / 800 mmHg
V2 = 95 ml.
Therefore, when the pressure of the argon gas increases to 800 mmHg, the volume occupied by the gas is 95 ml.