A gas at 1 atmosphere and having volume \(100 \mathrm{ml}\) is mixed with another gas of equal moles at \(0.5 \mathrm{~atm}\) and having \(50 \mathrm{ml}\) in flask of one litre, what is the final pressure? (A) \(0.125 \mathrm{~atm}\) (B) \(0.75 \mathrm{~atm}\) (C) 1 atm (D) \(0.5 \mathrm{~atm}\)

We are given that, Gas 1: Pressure (P1) = 1 atm, Volume (V1) = 100 ml Gas 2: Pressure (P2) = 0.5 atm, Volume (V2) = 50 ml Both gases have the same number of moles. Since volumes are given in ml, let's convert them to liters. V1 = 100 ml = 0.1 L V2 = 50 ml = 0.05 L Flask Volume (V) = 1 L

We know that PV = nRT, where n = number of moles, R = Universal Gas Constant, and T = temperature. We are given that both Gas 1 and Gas 2 have an equal number of moles. Let's call that number of moles x. As gas constant R and the temperature T are the same for both gases, we can ignore R and T in our calculations. We can write the relationship between pressure, volume, and moles for each gas as follows: P1 * V1 = x * (R * T) P2 * V2 = x * (R * T) Since x is equal for both gases, we can write: P1 * V1 = P2 * V2 Now, substitute the given values of P1, V1, P2, and V2, and solve for x: 1 atm * 0.1 L = 0.5 atm * 0.05 L

Solve the equation obtained in the previous step for x: 0.1 = 0.025 x = 0.1/0.025 = 4 moles Now, we have the equal number of moles (x) for both gases.

The total number of moles (n_total) would be equal to the sum of moles of Gas 1 and Gas 2: n_total = x + x = 2x Now, using the Ideal Gas Law formula (PV = nRT) to find the final pressure (P_total) in the 1 L flask: P_total * V = n_total * (R * T) As the volume of the flask (V) is 1 L, we can simplify the equation: P_total = n_total * (R * T) Substitute the value of n_total into the equation: P_total = 2 * 4 * (R * T) We can see that the term (R * T) is common in the pressure, volume, and moles relationship for both the gases, so we can use Gas 1's initial pressure and volume relationship to find P_total: 1 atm * 0.1 L = P_total * (R * T) Now substitute the value of n_total * (R * T) and solve for P_total: 1 atm * 0.1 L = 8 * (R * T) P_total = (1 * 0.1) / 8 = 0.0125 / 8 P_total = 0.75 atm So, the correct answer is: (B) 0.75 atm