0.052 moles of a gas has a pressure of 1.32 atm at 127 degree C. Calculate its Volume at STP
1 mole occupies 22.4L, so your gas fills (.052*22.4) = 1.16L
PV = kT
So, PV/T = k, a constant. Thus, you want V such that
1*V/273.15 = (1.32*(.052*22.4))/(273.15+127)
V = 1.05 L
makes sense, since it's getting cooled down
To calculate the volume of the gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Step 1: Convert the given temperature from Celsius to Kelvin.
The temperature in Kelvin (T) is given by:
T(°C) + 273.15 = T (K)
127 °C + 273.15 = 400.15 K
Step 2: Calculate the volume of the gas at STP.
Given:
Number of moles (n) = 0.052 moles
Pressure (P) = 1.32 atm
Temperature (T) = 400.15 K (converted from Celsius to Kelvin)
Using the ideal gas law equation, PV = nRT, we can rearrange it to solve for V:
V = (nRT) / P
Substituting the given values:
V = (0.052 moles * 0.0821 L.atm/mol.K * 400.15 K) / 1.32 atm
Calculating further:
V = 1.5875 liters (rounded to 4 decimal places)
Therefore, the volume of the gas at STP is approximately 1.5875 liters.
To calculate the volume at STP (Standard Temperature and Pressure), we need to use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, let's convert the given temperature from Celsius to Kelvin. The Kelvin temperature (T) is the Celsius temperature (127 °C) plus 273.15:
T = 127 °C + 273.15 = 400.15 K
Now, we have all the values needed for the equation except for the volume (V). However, since we want to find the volume at STP, we need to use the conditions of STP, which are:
- Pressure (P) = 1 atm
- Temperature (T) = 273.15 K
Now, we can rearrange the Ideal Gas Law equation to solve for V:
V = (nRT) / P
Substituting the values:
V = (0.052 moles * 0.0821 L·atm/mol·K * 400.15 K) / 1.32 atm
Before calculating the volume, let’s simplify the equation:
V = (0.052 * 0.0821 * 400.15) / 1.32
V ≈ 10.078 L
Therefore, the volume of the gas at STP is approximately 10.078 liters.