2gm of hydrogen are present in a closed vessel at S.T.P. If the same q...
Understanding the Given Problem
In this scenario, we have 2 g of hydrogen gas (H2) in a closed vessel at standard temperature and pressure (S.T.P). When another gas X is introduced, the total pressure rises to 1.5 atm.
Calculating Moles of Hydrogen
- The molar mass of hydrogen (H2) is approximately 2 g/mol.
- Therefore, moles of hydrogen = 2 g / 2 g/mol = 1 mol.
Using Ideal Gas Law
At S.T.P (1 atm, 273.15 K), 1 mole of any ideal gas occupies 22.4 L.
- The initial pressure due to hydrogen alone = 1 atm for 1 mol of H2.
When gas X is introduced, the total pressure becomes 1.5 atm. Thus,
Determining Contribution of Gas X
- The increase in pressure due to gas X = 1.5 atm - 1 atm = 0.5 atm.
Calculating Moles of Gas X
Using the ideal gas law (PV = nRT):
- Rearranging gives n = PV/RT.
- At S.T.P, R = 0.0821 L·atm/(K·mol) and T = 273.15 K.
For gas X, pressure = 0.5 atm, volume = 22.4 L:
- n = (0.5 atm * 22.4 L) / (0.0821 L·atm/(K·mol) * 273.15 K)
- This simplifies to approximately 0.5 mol of gas X.
Identifying Gas X
Now, we need to find a gas with a molar mass that fits with the moles calculated:
- CH4 (16 g/mol): 0.5 mol = 8 g → incorrect.
- SO2 (64 g/mol): 0.5 mol = 32 g → incorrect.
- O2 (32 g/mol): 0.5 mol = 16 g → incorrect.
- He (4 g/mol): 0.5 mol = 2 g → fits.
Thus, the correct identity of gas X is Helium (He).
2gm of hydrogen are present in a closed vessel at S.T.P. If the same q...
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