what pressure would have to be applied to a 27.2 ml sample of gas at 25 Celcius and 1.00atm to compress its volume to 1.ooml without a change in temperature
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Note the correct spelling of celsius.
P1V1 = P2V2
To find the pressure required to compress a gas, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (unknown in this case)
V = initial volume of the gas (27.2 mL)
n = number of moles of gas (unknown in this case)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (25°C + 273.15 = 298.15 K)
First, we need to find the initial number of moles in the gas sample using the ideal gas law equation:
n = PV / RT
Substituting the known values:
n = (1.00 atm * 27.2 mL) / (0.0821 L·atm/(mol·K) * 298.15 K)
Notice how we converted mL to L by dividing by 1000 since the ideal gas constant is in units of L, atm, and K.
n ≈ 1.09 x 10⁻³ mol
Now, we can use the initial number of moles (n) and the final volume of 1.00 mL to find the final pressure (P'):
PV = nRT
P' * 1.00 mL = (1.09 x 10⁻³ mol) * (0.0821 L·atm/(mol·K)) * 298.15 K
Notice how we converted mL to L by dividing by 1000 since the ideal gas constant is in units of L, atm, and K.
P' ≈ (1.09 x 10⁻³ mol * 0.0821 L·atm/(mol·K) * 298.15 K) / 1.00 mL
P' ≈ 0.0268 atm
Therefore, the pressure that would have to be applied to compress the gas sample to 1.00 mL without a change in temperature is approximately 0.0268 atm.