Answer:
The ideal gas law is a formula that relates the pressure, volume, temperature, and number of moles of a gas. It can be expressed as:
PV = nRT
where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature in Kelvin.
Since the number of moles and the temperature are constant in this problem, we can rearrange the formula to solve for the pressure:
P = (nRT) / V
Plugging in the known values, we get:
P = (nRT) / V
= (n * R * (35 + 273)) / 0.25 L
= (n * R * 308 K) / 0.25 L
We are given that the pressure is 500 mmHg and the volume is 0.25 L at this pressure, so we can set these equal:
500 mmHg = (n * R * 308 K) / 0.25 L
Solving for n, we get:
n = (500 mmHg * 0.25 L) / (R * 308 K)
We know that the pressure and volume of the gas at its original state are what we are trying to solve for. Let's call the original pressure P_0 and the original volume V_0. We can then express the relationship between the original and final state of the gas as:
P_0 * V_0 = n * R * T
Substituting the expression we found for n and the known values, we get:
P_0 * V_0 = ((500 mmHg * 0.25 L) / (R * 308 K)) * R * 308 K
Solving for P_0, we get:
P_0 = (500 mmHg * 0.25 L) / (R * 308 K) * (R * 308 K) / V_0
= (500 mmHg * 0.25 L) / (V_0)
Since V_0 = 0.5 L, we can substitute this value to get:
P_0 = (500 mmHg * 0.25 L) / (0.5 L)
= 500 mmHg / 2
= 250 mmHg
Therefore, the original pressure of the gas was 250 mmHg.