1.3 litre of Oxygen gas at 1 ATM and 300 kelvin is exposed to a solid ...
Calculation of x/m in Oxygen Gas AdsorptionGiven Data:
- Initial volume of Oxygen gas (Vi) = 1.3 L
- Initial pressure of Oxygen gas (Pi) = 1 ATM
- Final pressure of Oxygen gas (Pf) = 0.7 ATM
- Temperature of Oxygen gas (T) = 300 K
- Mass of adsorbent (m) = 3 g
Formula Used:
The amount of gas adsorbed (x) per unit mass of adsorbent (m) can be calculated using the following formula:
x/m = (1/V
i) * ln [(P
i - P
f) / P
f]
where,
ln = natural logarithm
Calculation:
Substituting the given values in the formula, we get:
x/m = (1/1.3) * ln [(1 - 0.7) / 0.7]
x/m = 0.769 * ln (0.4286)
x/m = 0.769 * (-0.8474)
x/m = -0.6529
Since x/m cannot be negative, we take the absolute value of the result.
x/m = 0.6529
Therefore, the value of x/m in the given oxygen gas adsorption problem is 0.6529.
Explanation:
The given problem deals with the adsorption of oxygen gas on a solid surface. The initial volume and pressure of the gas are given, and after complete adsorption, the pressure is reduced to a certain value. The amount of gas adsorbed per unit mass of adsorbent can be calculated using the formula x/m = (1/V
i) * ln [(P
i - P
f) / P
f].
This formula is derived from the ideal gas law and the Langmuir adsorption isotherm. The natural logarithm is used to account for the non-linear relationship between pressure and the amount of gas adsorbed. The value of x/m obtained from this formula gives an idea of the efficiency of the adsorbent in removing the gas from the system. In this case, we get a value of 0.6529, which means that the adsorbent is able to adsorb 0.6529 moles of oxygen gas per unit mass of adsorbent.