For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:

P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.

`P = k T`

`k = (P)/(T)`

Now, for comparing the same substance at two different conditions, this can be expressed as:

`(P_1)/(T_1) = (P_2)/(T_2)`

OR

`(P_1)(T_2) = (P_2)(T_1)`

From this we can solve the problem.

Given:

P1 = 760 mmHg -> initial pressure

T1 = 20 + 273.15 = 293.15K -> initial temperature

T2 = 55 + 273.15 = 328.15 K -> final temperature

P2 = x (unknown) -> final pressure

Substitute the given values and solve for the unknown:

`(P_1)(T_2) = (P_2)(T_1)`

(760)(328.15) = (x)(293.15)

x = (760*328.15)/(293.15)

**x = 851 mmHg**

Now, to get the number of moles, we will use the Ideal gas equation:

PV = nRT

n = number of moles = `(PV)/(RT)`

We can use any of the P and T sets, for this we shall use the T1 and P1.

Given:

P = 760 mmHg = 1 atm

V = 2600 Liters

R = 0.08201 atm-L / mol K

T = 293.15 K

`n = (1 * 2600)/(0.08201*293.15)`

**n = 108.08 moles = 108 moles**

For this problem, we can use the gas relationship between pressure and temperature at constant volume. This gas law is also called as the Gay-Lussac’s Law which states that:

P is directly proportional to T; as the pressure of the container increased, the total temperature will increase.

`P = k T`

`k = (P)/(T)`

Now, for comparing the same substance at two different conditions, this can be expressed as:

`(P_1)/(T_1) = (P_2)/(T_2)`

OR

`(P_1)(T_2) = (P_2)(T_1)`

From this we can solve the problem.

Given:

P1 = 760 mmHg -> initial pressure

T1 = 20 + 273.15 = 293.15K -> initial temperature

T2 = 55 + 273.15 = 328.15 K -> final temperature

P2 = x (unknown) -> final pressure

Substitute the given values and solve for the unknown:

`(P_1)(T_2) = (P_2)(T_1)`

(760)(328.15) = (x)(293.15)

x = (760*328.15)/(293.15)

**x = 851 mmHg**

Now, to get the number of moles, we will use the Ideal gas equation:

PV = nRT

n = number of moles = `(PV)/(RT)`

We can use any of the P and T sets, for this we shall use the T1 and P1.

Given:

P = 760 mmHg = 1 atm

V = 2600 Liters

R = 0.08201 atm-L / mol K

T = 293.15 K

`n = (1 * 2600)/(0.08201*293.15)`

**n = 108.08 moles = 108 moles**