Question

What is the pressure, in atmospheres, if the gas is warmed to a temperature of 31 deg * C and if and do not change?

Answer 1

To determine the pressure in atmospheres when the gas is warmed to a temperature of 31 degrees Celsius, we need to use the Ideal Gas Law equation:

PV = nRT

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

First, let's convert the given temperature from degrees Celsius to Kelvin:

T (Kelvin) = 31 + 273.15
T = 304.15 K

Assuming you meant "and volume do not change" in your question (since you only mentioned "if and do not change"), we can assume that the volume (V) remains constant.

Now, let's assume the number of moles (n) and the volume (V) are constant. Therefore, the equation becomes:

P1/T1 = P2/T2

where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure (what we need to find)
T2 = final temperature

Plugging the values:
P1 = P2
T1 = 273.15
T2 = 304.15

P1/T1 = P2/T2

P2 = (P1 * T2) / T1

Since P1 = P2:
P2 = (P2 * T2) / T1

Cross multiply:
P2 * T1 = P2 * T2

Divide both sides by P2:
T1 = T2

Therefore, the pressure in atmospheres is equal to the pressure before warming, which means there is no change in pressure.