A 250 L vessel is evacuated and then connected to a 50.0 L bulb with compressed nitrogen. The pressure in the combined containers is 1672 mm Hg. If the temperature remained at 20 °C throughout the process, what was the initial pressure in the 50.0 L bulb?

Question

A 250 L vessel is evacuated and then connected to a 50.0 L bulb with compressed nitrogen. The pressure in the combined containers is 1672 mm Hg. If the temperature remained at 20 °C throughout the process, what was the initial pressure in the 50.0 L bulb?

Can someone please give me a detailed explanation of how to solve this?

Answer 1

P1V1=P2V2

P1*250=1672mmHg*(250+50)
solve for P1

Answer 2

To solve this problem, we can apply the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the given temperature of 20 °C to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20 + 273.15
T(K) = 293.15 K

Now, let's solve for the initial pressure in the 50.0 L bulb. We'll assume that the number of moles and the temperature remain constant throughout the process:

P1V1 = nRT
P1(50.0 L) = n(0.0821 L·atm/mol·K)(293.15 K)
50.0P1 = 24.8356n (eq. 1)

Next, let's consider the combined containers (the 250 L vessel and the 50.0 L bulb) after they are connected. Since the vessel was initially evacuated, there were no gas molecules present. Therefore, the number of moles in the combined containers is equal to the number of moles initially present in the 50.0 L bulb:

n_initial = n_combined

We can use the ideal gas law to find the pressure in the combined containers:

P2V2 = n_combinedRT
P2(300.0 L) = n_combined(0.0821 L·atm/mol·K)(293.15 K)
300.0P2 = 24.8356n_combined (eq. 2)

Now, we know that the combined pressure is 1672 mm Hg. We can convert this pressure to atm:

1 atm = 760 mm Hg
1672 mm Hg = 1672/760 atm
P_combined = 2.2 atm

Substituting this value into eq. 2:

300.0(2.2 atm) = 24.8356n_combined
660.0 atm = 24.8356n_combined
26.5552n_combined = 660.0 atm
n_combined = 24.8356 mol

Since n_initial = n_combined, we can use eq. 1 to find the initial pressure in the 50.0 L bulb:

50.0P1 = 24.8356( eq. 1 )
50.0P1 = 596.778
P1 = 596.778/50.0
P1 = 11.93556 atm

Therefore, the initial pressure in the 50.0 L bulb is approximately 11.94 atm.

A 250 L vessel is evacuated and then connected to a 50.0 L bulb with compressed nitrogen. The pressure in the combined containers is 1672 mm Hg. If the temperature remained at 20 °C throughout the process, what was the initial pressure in the 50.0 L bulb?

P1V1=P2V2

2.64?

To solve this problem, we can apply the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.