A bacterial culture isolated from sewage produced 35.5 mL of methane, CH4, at 31oC and 1 atm. What is the volume of this methane at standard temperature and pressure?
Use (P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To calculate the volume of methane, CH4, at standard temperature and pressure, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature in Kelvin
In the given question, we are given the volume of methane produced (35.5 mL), temperature (31°C), and pressure (1 atm). However, we need to convert the temperature to Kelvin before using it in the equation.
To convert temperature from Celsius to Kelvin, we use the formula: K = °C + 273
So, the temperature in Kelvin is: T = 31°C + 273 = 304 K
Now, we need to calculate the number of moles of methane.
To do this, we can use the ideal gas law equation in rearranged form:
n = PV / RT
Substituting the values we have:
n = (1 atm * 35.5 mL) / (0.0821 L·atm/mol·K * 304 K)
Now, let's calculate the moles of methane:
n = (1 * 35.5) / (0.0821 * 304)
= 1.39 moles
Since at standard temperature and pressure (STP) 1 mole occupies 22.4 L of volume, we can calculate the volume of methane at STP:
Volume at STP = n * 22.4 L
Volume at STP = 1.39 * 22.4 = 31.2 L
Therefore, the volume of methane at standard temperature and pressure is 31.2 L.
To find the volume of methane at standard temperature and pressure (STP), we can use the concept of ideal gas laws. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature (in Kelvin)
At STP, the temperature is 273.15 K, and the pressure is 1 atm. We need to convert these values to the proper units before plugging them into the equation.
Given:
Initial Volume (V1) = 35.5 mL
Initial Temperature (T1) = 31°C = 31 + 273.15 K
Initial Pressure (P1) = 1 atm
Final Temperature (T2) = 273.15 K (STP temperature)
Final Pressure (P2) = 1 atm (STP Pressure)
First, let's convert the initial temperature from °C to Kelvin:
T1 = 31 + 273.15
T1 = 304.15 K
Now we can calculate the number of moles of methane using the ideal gas law equation.
PV = nRT
n = (PV) / (RT)
n1 = (P1V1) / (R * T1)
Substituting the values:
n1 = (1 atm * 35.5 mL) / (0.0821 L * atm / mol * K * 304.15 K)
Note: We converted mL to L by dividing by 1000.
n1 = 0.0014 mol
Now, let's calculate the final volume at STP using the equation:
n2 = n1 * (P2 / P1) * (T1 / T2)
n2 = 0.0014 mol * (1 atm / 1 atm) * (304.15 K / 273.15 K)
n2 = 0.0014 mol
Therefore, the volume of methane at standard temperature and pressure (STP) is equal to the initial volume:
V2 = V1 = 35.5 mL
Therefore, the volume of methane at STP is 35.5 mL.