If 0.117 mol of argon gas occupies 2.15 L at 725 mmHg, what is the temperature in degrees Celsius?
please explain step by step.
Thank you so much
Use PV = nRT
T will be in Kelvin. Solve for C by
K = 273 + C.
To find the temperature in degrees Celsius, we need to use the ideal gas law equation: PV = nRT. Here's how to proceed step by step:
Step 1: Gather the given values:
- Volume (V) = 2.15 L
- Pressure (P) = 725 mmHg
- Number of moles (n) = 0.117 mol
Step 2: Convert the pressure to atm:
Since the ideal gas law equation requires pressure in atm, we need to convert 725 mmHg to atm. The conversion factor is as follows:
1 atm = 760 mmHg
To convert mmHg to atm, divide the given pressure by 760:
725 mmHg / 760 mmHg = 0.954 atm
Now we can use the converted pressure value in the ideal gas law equation.
Step 3: Convert the volume to liters:
The given volume is already in liters, so no conversion is needed.
Step 4: Convert the temperature to Kelvin:
The ideal gas law equation requires temperature in Kelvin, so we need to convert from Celsius to Kelvin. The conversion formula is as follows:
Kelvin = Celsius + 273.15
Step 5: Rearrange the ideal gas law equation to solve for temperature:
The ideal gas law equation is given as PV = nRT. We can rearrange it to solve for temperature (T):
T = PV / (nR)
Step 6: Calculate the temperature:
Plug in the values into the rearranged ideal gas law equation:
T = (0.954 atm) * (2.15 L) / (0.117 mol * R)
Note: R is the ideal gas constant, which has a value of 0.0821 L·atm/(mol·K).
T = (0.954 atm * 2.15 L) / (0.117 mol * 0.0821 L·atm/(mol·K))
The units of L and mol cancel out, leaving temperature in Kelvin:
T = 22.029 K
Step 7: Convert Kelvin to Celsius:
To convert from Kelvin to Celsius, subtract 273.15 from the calculated temperature:
T = 22.029 K - 273.15 = -251.121 °C
Therefore, the temperature in degrees Celsius is approximately -251.121°C.