A 100 mL flask contained `H_(2)` at 200 Torr, and a 200 mL flask contained He at 100 Torr. The two flask were then connected so that each gas filled their combined volume. Assuming no change in temperature,total pressure is

Options

A. 300 Torr
B. 66.66 Torr
C. 150 Torr
D. 133.33 Torr

Explanation

To solve the problem, we will use the ideal gas law and the principle of partial pressures. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Data
- For Hydrogen (H₂):
- Volume (V₁) = 100 mL
- Pressure (P₁) = 200 Torr

- For Helium (He):
- Volume (V₂) = 200 mL
- Pressure (P₂) = 100 Torr

### Step 2: Calculate the Number of Moles for Each Gas
Using the ideal gas equation \( PV = nRT \), we can express the number of moles (n) as:
\[ n = \frac{PV}{RT} \]

#### For Hydrogen (H₂):
\[ n_1 = \frac{P_1 V_1}{RT} = \frac{200 \, \text{Torr} \times 100 \, \text{mL}}{RT} \]

#### For Helium (He):
\[ n_2 = \frac{P_2 V_2}{RT} = \frac{100 \, \text{Torr} \times 200 \, \text{mL}}{RT} \]

### Step 3: Combine the Volumes
When the two flasks are connected, the total volume (V_total) is:
\[ V_{total} = V_1 + V_2 = 100 \, \text{mL} + 200 \, \text{mL} = 300 \, \text{mL} \]

### Step 4: Calculate the Total Number of Moles
The total number of moles (n_total) is the sum of the moles of each gas:
\[ n_{total} = n_1 + n_2 = \frac{200 \times 100}{RT} + \frac{100 \times 200}{RT} \]
\[ = \frac{20000 + 20000}{RT} = \frac{40000}{RT} \]

### Step 5: Calculate the Total Pressure
Using the ideal gas law again for the combined system:
\[ P_{total} V_{total} = n_{total} RT \]
Substituting the values:
\[ P_{total} \times 300 = \frac{40000}{RT} \times RT \]
\[ P_{total} \times 300 = 40000 \]
\[ P_{total} = \frac{40000}{300} = \frac{400}{3} \approx 133.33 \, \text{Torr} \]

### Final Answer
The total pressure after connecting the two flasks is approximately **133.33 Torr**.

---