How many molecules of N2 gas can be present in a 2.5 L flask at 50°C and 650 mmHg (R = 0.08206 L·atm·K-1·mol-1, 1 atm = 760 mmHg, 1 mole = 6.022 × 1023 molecules)?
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.08206 L·atm·K-1·mol-1)
T = temperature (in K)
First, we need to convert the given pressure to atm:
650 mmHg * (1 atm / 760 mmHg) = 0.8553 atm
Next, we convert the temperature from Celsius to Kelvin:
50°C + 273 = 323 K
Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
n = (0.8553 atm * 2.5 L) / (0.08206 L·atm·K-1·mol-1 * 323 K)
n ≈ 0.084 moles
Finally, we can convert moles to molecules using Avogadro's number:
0.084 moles * 6.022 × 10^23 molecules/mole ≈ 5.06 × 10^22 molecules
Therefore, there are approximately 5.06 × 10^22 molecules of N2 gas present in the 2.5 L flask at 50°C and 650 mmHg.