A tank of helium gas with a pressure of 210 torr at 0∘C is heated to give a pressure of 1100 torr .
I don't see a question here. Probably you want to know T2.
(P1/T1) = (P2/T2)
T1 and T2 are in Kelvin.
To solve this problem, we can use the combined gas law equation, which relates the initial and final conditions of a gas when its temperature, pressure, and volume change.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes,
T1 and T2 are the initial and final temperatures.
Let's assume the initial and final volumes are constant.
Given:
P1 = 210 torr (initial pressure)
T1 = 0°C (initial temperature)
P2 = 1100 torr (final pressure)
We need to find T2 (final temperature).
Converting the temperatures from °C to Kelvin:
T1 = 0 + 273.15 = 273.15 K
Now we can rearrange the equation to solve for T2:
(P1 * V1) / T1 = (P2 * V2) / T2
Since V1 = V2, we can simplify the equation:
P1 / T1 = P2 / T2
Now we can plug in the values:
210 torr / 273.15 K = 1100 torr / T2
Cross-multiplying:
(P1 * T2) = (P2 * T1)
(210 torr) * T2 = (1100 torr) * (273.15 K)
Dividing both sides by 210 torr:
T2 = (1100 torr * 273.15 K) / 210 torr
T2 ≈ 1427.31 K
Therefore, when the tank of helium gas is heated, the temperature will be approximately 1427.31 K.
To find the final temperature of the helium gas after it is heated, we can 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)
In this case, we are given the initial pressure (210 torr) at 0°C and the final pressure (1100 torr). To solve for the temperature, let's follow these steps:
Step 1: Convert the given temperatures to Kelvin.
Since we are given the temperature in degrees Celsius, we need to convert it to Kelvin by adding 273.15.
Initial temperature (0°C) = 0 + 273.15 = 273.15 K
Step 2: Convert the pressures from torr to atmospheres.
Since the ideal gas law uses pressure in atmospheres, we need to convert torr to atmospheres by dividing by 760.
Initial pressure (210 torr) = 210/760 = 0.276 atm
Final pressure (1100 torr) = 1100/760 = 1.447 atm
Step 3: Rearrange the ideal gas law equation to solve for temperature (T).
PV = nRT
T = PV / (nR)
Step 4: Calculate the final temperature.
Substitute the values into the equation and solve.
Initial pressure (P1) = 0.276 atm
Final pressure (P2) = 1.447 atm
Initial temperature (T1) = 273.15 K
n = number of moles (Since the number of moles is not given, we can assume it remains constant throughout the process.)
R = 0.0821 L·atm/mol·K
T2 = P2V / (P1V) * T1
T2 = (1.447 * V) / (0.276 * V) * 273.15
T2 ≈ 1414 K
Therefore, the final temperature of the helium gas after it is heated is approximately 1414 K.