Answer
418.2k+ 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
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)