Answer
405.3k+ views
Hint: This problem is based on the concept of mixing of solutions. The concentration, pressure, and volume of the resulting mixture will surely be different from either and hence, there is a formula to determine the same. The ideal gas equation is an equation for hypothetical gas wherein all the conditions of pressure, temperature, volume, and amount of gas is constant for all the gases.Hence, the gas is called ideal gas and the law as ideal gas law.
The ideal gas equation is given as,
$PV = nRT$
Here, P $ = $PRESSURE OF THE GAS
V $ = $ volume of the gas
n $ = $ no. of moles of gas
R $ = $ universal gas constant
T $ = $ Temperature
Complete step by step solution:
Given –
The volume of gas A (${V_A}$) $ = $ 1000 $mL$
The volume of gas B (${V_B}$) $ = $500 $mL$
The pressure of gas A (${P_A}$) $ = $600 $torr$
The pressure of gas B (${P_B}$) $ = $800 $torr$
The volume of the resulting mixture (${V_M}$) $ = $ 2 $Litre$$ = $ 2000 $mL$
To find, according to the ideal gas equation, $PV = nRT$
The pressure of the resulting mixture (${P_M}$) $ = $ ?
In the given question, Pressure and volume are given and the values of n and R are constant for a given equation.
Also, in the given problem, Temperature T is a constant
Hence,
PV$ = $ constant
$\Rightarrow P \propto V$ (According to Boyle’s law)
According to the formula,
${P_M}{V_M} = {P_A}{V_A} + {P_B}{V_B}$
Now we have to find out the pressure of the resulting mixture,
$\Rightarrow {P_M} = \dfrac{{{P_1}{V_1} + {P_2}{V_2}}}{{{V_M}}}$
Substituting the values as given in the question,
$\Rightarrow {P_M} = \dfrac{{\left( {600} \right)\left( {1000} \right) + \left( {800} \right)\left( {500} \right)}}{{2000}}$
$\Rightarrow {P_M} = \dfrac{{600000 + 400000}}{{2000}}$
$\Rightarrow {P_M} = \dfrac{{1000000}}{{2000}}$
$\Rightarrow {P_M} = 500torr$
Hence the pressure of the resulting mixture will be 500 $torr$
So, the correct answer is Option A.
Note: As the temperature and other values are constant and favorable, the question is quite easily solvable. If the values were not constant then the formula would have changed.
Boyle’s law states that the pressure is inversely proportional to volume for gas if the conditions for temperature and amount of gas are constant.
The ideal gas equation is given as,
$PV = nRT$
Here, P $ = $PRESSURE OF THE GAS
V $ = $ volume of the gas
n $ = $ no. of moles of gas
R $ = $ universal gas constant
T $ = $ Temperature
Complete step by step solution:
Given –
The volume of gas A (${V_A}$) $ = $ 1000 $mL$
The volume of gas B (${V_B}$) $ = $500 $mL$
The pressure of gas A (${P_A}$) $ = $600 $torr$
The pressure of gas B (${P_B}$) $ = $800 $torr$
The volume of the resulting mixture (${V_M}$) $ = $ 2 $Litre$$ = $ 2000 $mL$
To find, according to the ideal gas equation, $PV = nRT$
The pressure of the resulting mixture (${P_M}$) $ = $ ?
In the given question, Pressure and volume are given and the values of n and R are constant for a given equation.
Also, in the given problem, Temperature T is a constant
Hence,
PV$ = $ constant
$\Rightarrow P \propto V$ (According to Boyle’s law)
According to the formula,
${P_M}{V_M} = {P_A}{V_A} + {P_B}{V_B}$
Now we have to find out the pressure of the resulting mixture,
$\Rightarrow {P_M} = \dfrac{{{P_1}{V_1} + {P_2}{V_2}}}{{{V_M}}}$
Substituting the values as given in the question,
$\Rightarrow {P_M} = \dfrac{{\left( {600} \right)\left( {1000} \right) + \left( {800} \right)\left( {500} \right)}}{{2000}}$
$\Rightarrow {P_M} = \dfrac{{600000 + 400000}}{{2000}}$
$\Rightarrow {P_M} = \dfrac{{1000000}}{{2000}}$
$\Rightarrow {P_M} = 500torr$
Hence the pressure of the resulting mixture will be 500 $torr$
So, the correct answer is Option A.
Note: As the temperature and other values are constant and favorable, the question is quite easily solvable. If the values were not constant then the formula would have changed.
Boyle’s law states that the pressure is inversely proportional to volume for gas if the conditions for temperature and amount of gas are constant.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)