Answer:
the pressure of the O2 in the flask is 0.721 torr.
Step-by-step explanation:
We can use the Ideal Gas Law to solve this problem, which states:
PV = nRT
where P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles of gas, R is the gas constant (0.08206 L·atm/mol·K), and T is the temperature in Kelvin (K).
To use this equation, we need to convert the given volume and temperature to the appropriate units:
Volume: 157 mL = 0.157 L
Temperature: 12°C = 285 K (273 + 12)
Next, we need to calculate the number of moles of oxygen (O2) using the mass given:
mass of O2 = 2.1 µg = 2.1 × 10^-6 g
molar mass of O2 = 32 g/mol
n = (2.1 × 10^-6 g) / (32 g/mol) = 6.56 × 10^-8 mol
Now we can substitute the known values into the Ideal Gas Law:
PV = nRT
P(0.157 L) = (6.56 × 10^-8 mol)(0.08206 L·atm/mol·K)(285 K)
Simplifying, we get:
P = [(6.56 × 10^-8 mol)(0.08206 L·atm/mol·K)(285 K)] / (0.157 L)
P = 0.000949 atm
Finally, we can convert from atmospheres to torr using the conversion factor 1 atm = 760 torr:
P = 0.000949 atm × 760 torr/atm
P = 0.721 torr
Therefore, the pressure of the O2 in the flask is 0.721 torr.