COMEDK 2023 Shift 1 Paper

To find the molecular mass of the unknown gas, we will use the Ideal Gas Law and the concept of molar mass. The Ideal Gas Law is given by:
PV=nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the universal gas constant
T is the temperature of the gas in Kelvin
Let's start by converting the temperatures given in degrees Celsius to Kelvin:
‌T‌unknown ‌=95∘C=95+273.15=368.15K
‌T‌hydrogen ‌=17∘C=17+273.15=290.15K
According to the problem, the volume and the pressure of both gases are the same. Thus, from the Ideal Gas Law:
n‌unknown ‌‌‌RT‌unknown ‌=n‌hydrogen ‌‌‌RT‌hydrogen ‌
Since R is constant, it cancels out. Rearranging the equation, we get:
n‌unknown ‌‌‌T‌unknown ‌=n‌hydrogen ‌‌‌T‌hydrogen ‌
To find the moles of each gas, we use the relation between the mass and the molar mass:
n=‌

m

‌ Molar Mass ‌

For hydrogen (H2), the molar mass is approximately 2g∕mol.
n‌hydrogen ‌=‌

0.368g

2g∕mol

=0.184‌mol
Substituting the values into the equation, we get:
‌

m‌unknown ‌

M‌unknown ‌

×368.15K=0.184‌mol×290.15K
Where m‌unknown ‌‌‌=5.8g and M‌unknown ‌‌‌ is the molar mass of the unknown gas which we need to find.
Solving, we have:
‌‌

5.8

M‌unknown ‌

×368.15=0.184×290.15
‌‌

5.8×368.15

M‌unknown ‌

=53.3876
‌M‌unknown ‌=‌

5.8×368.15

53.3876

≈40g∕mol
Thus, the molecular mass of the unknown gas is approximately 40g∕mol, which corresponds to option (D).