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If 1000mL of gas A at 600torr and 500mL of gas B at 800 torr are mixed in a 2Litre flask, the pressure of the mixture at constant temperature will be –(A) 500 $torr$(B) 1000 $torr$(C) 850 $torr$(D) 2000 $torr$

Last updated date: 22nd Jun 2024
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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.