A flask that can withstand an internal pressure of 2488 torr, but no more, is filled with a gas at 21.0°C and 758 torr and heated. At what temperature will it burst?
To determine the temperature at which the flask will burst, we need to use the ideal gas law equation, which relates the pressure, volume, number of moles, and temperature of a gas.
The ideal gas law equation is given as:
PV = nRT
Where:
P = pressure (in this case, in torr)
V = volume (assumed constant in this case)
n = number of moles of gas (assumed constant in this case)
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in kelvin)
In this case, the volume and number of moles of gas are assumed constant. We need to determine the temperature at which the pressure reaches the bursting point, which is 2488 torr.
First, convert the initial temperature of the gas (21.0°C) to kelvin:
T_initial = 21.0°C + 273.15 = 294.15 K
Next, use the initial pressure and temperature in the ideal gas law equation to find the initial number of moles of gas:
n_initial = (P_initial * V) / (R * T_initial)
Since the volume and number of moles of gas are constant, we can rewrite the equation as:
P_initial / T_initial = n_initial * R / V
Now, rearrange the equation to solve for the final temperature at which the pressure reaches the bursting point (T_final):
T_final = (P_final * V) / (n_initial * R)
Plugging in the given values:
P_final = 2488 torr
V = (assumed constant)
n_initial = (assumed constant)
R = 0.0821 L·atm/(mol·K)
T_final = (2488 torr * V) / (n_initial * 0.0821 L·atm/(mol·K))
Since the volume and number of moles of gas are assumed constant, we can simplify the equation to:
T_final = (2488 torr * V) / (n_initial * 0.0821 L·atm/(mol·K))
Note: The specific values for volume and number of moles were not given in the question. If they were provided, you would substitute them into the equation. If they were not provided, you would need more information to calculate them.
So, without knowing the specific values for volume and number of moles, it is not possible to determine the exact temperature at which the flask will burst.
(P1/T1) = (P2/T2)
Solve for T2 and convert to C.