500ml of gas at 20 degrees celcius is under a pressure of 100cm of mercury what would be its volume at s.t.p?
you know that PV/T is constant. So, you want P where
(100)(500)/(293.15) = P(22400)/(273.15)
To find the volume of gas at STP (Standard Temperature and Pressure), we can apply the combined gas law, which states that the product of the initial pressure, initial volume, and initial temperature is equal to the product of the final pressure, final volume, and final temperature.
Given:
Initial pressure (P): 100 cm Hg
Initial volume (V): 500 ml
Initial temperature (T): 20 degrees Celsius
STP conditions:
Final pressure (P'): 1 atm
Final temperature (T'): 0 degrees Celsius
Using the combined gas law formula:
(P * V)/T = (P' * V')/T'
Converting the units:
100 cm Hg = 1.3158 atm
500 ml = 0.5 L
20 degrees Celsius = 293.15 K
1 atm = 273.15 K
Substituting the values into the equation:
(1.3158 atm * 0.5 L)/293.15 K = (1 atm * V')/273.15 K
Simplifying the equation:
0.6579/293.15 = 1/273.15
Cross-multiplying:
0.6579 * 273.15 = 293.15 * V'
Solving for V':
V' = (0.6579 * 273.15)/(293.15)
V' = 0.614 L
Therefore, the volume of the gas at STP would be approximately 0.614 L.
To find the volume of gas at standard temperature and pressure (STP), 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 in Kelvin
First, we need to convert the given temperature from degrees Celsius to Kelvin. The conversion equation is:
T(K) = T(°C) + 273.15
So, 20°C + 273.15 = 293.15 K
The given pressure is 100 cmHg. However, for the ideal gas law equation, we need to convert it to the SI unit of pressure, which is Pascals (Pa). The conversion factor is:
1 cmHg = 133.32 Pa
Therefore, 100 cmHg × 133.32 Pa/cmHg = 13332 Pa
Now, we have:
P = 13332 Pa
V = 500 mL
To find the volume at STP, we need to calculate the number of moles (n) using the equation:
n = PV / RT
The ideal gas constant (R) is 8.314 J/(mol·K).
Next, we need to convert the volume from milliliters (mL) to liters (L):
1 L = 1000 mL
500 mL / 1000 mL/L = 0.5 L
Substituting the given values into the equation:
n = (13332 Pa) * (0.5 L) / (8.314 J/(mol·K) * 293.15 K)
After performing the calculation, we can find the value of n.
Finally, to find the volume at STP, we can rearrange the ideal gas law equation:
V(STP) = n(STP) * R * T(STP) / P(STP)
At STP, the conditions are:
P(STP) = 1 atmosphere = 101325 Pa
T(STP) = 273.15 K
Substituting the known values into the equation, we can calculate V(STP).