Synthetic diamonds can be manufactured at pressures of 6.00 x 104 atm. If we took 2.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 104 atm, what would the volume of that gas be?
There were 2 liters :)
Assuming it does not get a little hot:
P V = n R T
assume here n , R , T constant
so
P V = constant
P1 V1 = P2 V2
1 atm * 2 liters = 6 * 10^4 atm * x liters
x = (1/3)* 10^-4 liters = 0.000033333 liters = 0.033333 milliliters = not much
To find the volume of gas after compression, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas (assumed to be constant for this problem)
Given:
Initial pressure (P1) = 1.00 atm
Initial volume (V1) = 2.00 liters
Final pressure (P2) = 6.00 x 10^4 atm
Since the number of moles and the temperature are constant, we can rewrite the equation as:
P1V1 = P2V2
Solving for V2 (final volume):
V2 = (P1V1) / P2
Substituting the given values:
V2 = (1.00 atm * 2.00 L) / (6.00 x 10^4 atm)
To determine the final volume of the gas after compression, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when temperature is constant.
Boyle's Law equation:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (in atm)
V1 = initial volume (in liters)
P2 = final pressure (in atm)
V2 = final volume (in liters)
Given values:
P1 = 1.00 atm
V1 = 2.00 liters
P2 = 6.00 x 10^4 atm
Let's solve for V2:
P1 * V1 = P2 * V2
1.00 atm * 2.00 L = (6.00 x 10^4 atm) * V2
2.00 L = (6.00 x 10^4 atm) * V2
V2 = 2.00 L / (6.00 x 10^4 atm)
V2 = 3.33 x 10^-5 L
Therefore, when the gas is compressed to a pressure of 6.00 x 10^4 atm, its volume would be approximately 3.33 x 10^-5 liters.