A 6.7l volume of air,initially at 23.c and 0.98atm, is compressed to 2.7l while heated to 125 .c. which is the final pressure?

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin

First, we need to convert the initial and final temperatures from Celsius to Kelvin:

Initial temperature (T1) = 23°C + 273.15 = 296.15 K
Final temperature (T2) = 125°C + 273.15 = 398.15 K

Next, we can calculate the initial number of moles (n1) using the ideal gas law equation:

P1V1 = n1RT1

n1 = (P1V1) / (RT1)

Given:
P1 = 0.98 atm
V1 = 6.7 L
T1 = 296.15 K
R = 0.0821 L·atm/(mol·K)

n1 = (0.98 atm * 6.7 L) / (0.0821 L·atm/(mol·K) * 296.15 K)
n1 ≈ 0.285 mol

Now, we can use the ideal gas law equation to find the final pressure (P2):

P2V2 = n2RT2

Since the number of moles (n2) remains constant, we can rewrite the equation as:

P2 = (n1 * R * T2) / V2

Given:
n1 = 0.285 mol
R = 0.0821 L·atm/(mol·K)
T2 = 398.15 K
V2 = 2.7 L

P2 = (0.285 mol * 0.0821 L·atm/(mol·K) * 398.15 K) / 2.7 L
P2 ≈ 10.5 atm

Therefore, the final pressure is approximately 10.5 atm.