32 gram of O2, 28 gram of N2 and 16 gram of ch4 have different masses but same volume .why?
Answers
Answer:
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The given gases have different mass but the same volume because of the difference in molar mass.
Given,
molecular mass of O2 = 32 g
molecular mass of N2 = 28 g
molecular mass of CH4 = 16 g
To Find,
reason why their volumes are the same
Solution,
We can solve this using the following method.
We use the ideal gas equation for solving this equation.
The ideal gas equation is given as:
⇒ PV = nRT
where P is the pressure of the gas,
V is the volume of the gas,
n is the no. of moles of the gas,
R is the Gas constant,
T is the temperature in K.
Here, the the no. of moles of the gas could be expressed in terms of its molecular mass 'm' and molar mass 'M' as:
⇒ n = m/M
Therefore, the ideal gas law could be rewritten as:
⇒ PV = (m/M)RT
From this, we could find the equation for volume of a gas.
⇒ V = (m/M)(RT/P)
⇒ V = (m/M)k liters
where k is a constant, and k = RT/P.
We have 3 gases under consideration.
Gas 1: 32 grams of O2
m = 32 g
M = 16 + 16 = 32 g/mol
⇒ V = (32/32)k
⇒ V = k liters
Gas 2: 28 grams of N2
m = 28 g
M = 14 + 14 = 28 g/mol
⇒ V = (38/38)k
⇒ V = k liters
Gas 3: 16 grams of CH4
m = 16 g
M = 12 + 4×1 = 12 + 4 = 16 g/mol
⇒ V = (16/16)k
⇒ V = k liters
Therefore, the volumes of these gases are the same, even though they have different masses.
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