The volume of a flask is 300.0 mL, the pressure in the room is 770 mmHg and the temperature is 22.0°C. How many moles of CO2 are in the flask?
PV = nRT
To determine the number of moles of CO2 in the flask, we will use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)
First, let's convert the given values into appropriate units:
The volume of the flask is given as 300.0 mL. Since the ideal gas law equation requires the volume in liters, we need to convert mL to L. There are 1000 mL in 1 L, so:
Volume (V) = 300.0 mL / 1000 = 0.300 L
The pressure in the room is given as 770 mmHg. To convert it to atmospheres (atm), we need to divide it by the conversion factor of 760 mmHg/atm:
Pressure (P) = 770 mmHg / 760 mmHg/atm = 1.01316 atm
The temperature is given as 22.0°C. To convert it to Kelvin, we need to add 273.15 to the Celsius value:
Temperature (T) = 22.0°C + 273.15 = 295.15 K
Now we can substitute the values into the ideal gas law equation and solve for the number of moles (n):
(1.01316 atm) x (0.300 L) = n x (0.0821 L·atm/(mol·K)) x (295.15 K)
Note: Cross out matching units, in this case, liters (L) and atmospheres (atm).
Simplifying the equation:
0.30415 atm·L = n x (24.217115 L·atm/(mol·K))
Divide both sides by (24.217115 L·atm/(mol·K)):
n = (0.30415 atm·L) / (24.217115 L·atm/(mol·K))
n = 0.0125667 mol
Therefore, there are approximately 0.0126 moles of CO2 in the flask.