Question

4g argon (Atomic mass = 40) in a bulb at a temperature of TK has a pressure P atm. When the bulb was placed hot at a temperature $50^\circ C$ more than the first one, 0.8 g of gas had to be removed to get the original pressure. T is equal to:
A. 510 K
B. 200 K
C. 100 K
D. 73 K

Answer 1

In the question, we need to use the ideal gas equation formula. The mass of the argon changes on heating and the new mass will be 3.2 g. Both the conditions before and after the heating is compared to get the temperature.

Complete step by step answer:
Given,
Mass of argon is 4g.
Atomic mass 40.
The mass of gas removed is 0.8 g.
Here, the ideal gas equation is used.
The ideal gas equation is applied on ideal gases. It explains the behavior of gases under different conditions.
The ideal gas equation is given by the formula as shown below.
$PV = nRT$
Where,
P is the pressure
V is the volume
n is the number of moles
R is the universal gas constant.
T is the temperature
The number of moles is calculated as shown below.
$n = \dfrac{m}{M}$
n is the number of moles.
m is the mass
M is the molecular weight.
Substitute the values in the above equation.
$\Rightarrow {P_1}V = \dfrac{4}{{40}}RT$
$\Rightarrow {P_1} = \dfrac{4}{{40V}}RT$
It is given that the bulb was placed in hot at a temperature $50^\circ C$ and 0.8 g of gas had to be removed to get the original pressure
So the mass will be 4 g – 0.8 g = 3.2 g.
Substitute the new mass in the equation.
$\Rightarrow {P_2} = \dfrac{{3.2}}{{40V}}R(T + 50)$
${P_1} = {P_2}$
Substitute the values in the above relation.
$\Rightarrow \dfrac{4}{{40V}}RT = \dfrac{{3.2}}{{40V}}R(T + 30)$
$\Rightarrow 40T = 32(T + 50)$
$\Rightarrow 40T - 30T = 50 \times 32$
$\Rightarrow T = \dfrac{{50 \times 32}}{8}$
$\Rightarrow T = 200K$
Thus, T is equal to 200 k.
Therefore, the correct option is B.

Note:
The value of mass and molecular weight is given, so don't be confused as we don’t need to find the number of moles, we need to find the resulting temperature by the two relations.