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=nRTWhere:
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=368.15K‌T‌hydrogen ‌=17∘C=17+273.15=290.15KAccording 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=‌For hydrogen
(H2), the molar mass is approximately
2g∕mol.
n‌hydrogen ‌=‌=0.184‌mol Substituting the values into the equation, we get:
‌| m‌unknown ‌ |
| M‌unknown ‌ |
×368.15K=0.184‌mol×290.15KWhere
m‌unknown ‌‌‌=5.8g and
M‌unknown ‌‌‌ is the molar mass of the unknown gas which we need to find.
Solving, we have:
‌‌×368.15=0.184×290.15‌‌| 5.8×368.15 |
| M‌unknown ‌ |
=53.3876‌M‌unknown ‌=‌≈40g∕molThus, the molecular mass of the unknown gas is approximately
40g∕mol, which corresponds to option (D).