Final answer:
The number of molecules in 760 cc of gas at 0°C and 700mm pressure is approximately 1.88 x 10²². This is calculated by adjusting the volume to STP conditions and then using Avogadro's law. The correct answer is option a.
Step-by-step explanation:
The number of molecules present in a given volume of gas can be determined using Avogadro's law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. At standard temperature and pressure (STP), 1 mole of an ideal gas occupies 22.41 L. The STP conditions are defined as a temperature of 0°C and a pressure of 1 atm. The question states a volume of 760 cc (or 0.76 L) and a pressure of 700 mmHg which is nearly equal to 1 atm (760 mmHg).
First, we need to correct the volume to standard pressure using Boyle's Law since the conditions given are not STP but close. Assuming the temperature remains constant, when a gas at a pressure of 700 mmHg occupies 760 cc, it would occupy a volume V2 when the pressure is changed to 760 mmHg (1 atm).
V1 × P1 = V2 × P2
V2 = (V1 × P1) / P2
V2 = (760 cc × 700 mmHg) / 760 mmHg
V2 = (760 cc × 700) / 760
V2 = 700 cc
Now, we calculate the number of moles (n) at STP:
n = V / 22.41 L
n = 0.7 L / 22.41 L/mol
n ≈ 0.0312 moles
Finally, using Avogadro's number (6.02 x 1023 molecules/mol), we calculate the number of molecules present:
Number of molecules = n × Avogadro's number
Number of molecules ≈ 0.0312 moles × 6.02 x 1023 molecules/mol
Number of molecules ≈ 1.88 x 1022 molecules
The correct answer is (a) 1.88 x 1022 molecules.