A certain amount of gas at 27.0°C and at a pressure of 0.850 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.45 atm. How high can you raise the temperature of the gas without bursting the vessel? In other words, at what temperature will the glass vessel shatter, in degrees Celsius?

591.7°C

Explanation:

Data obtained from the question include:

T1 (initial temperature) = 27°C = 27 + 273 = 300K

P1 (initial pressure) = 0.850 atm

P2 (final pressure) = 2.45 atm

T2 (final temperature) =?

Using the equation P1/T1 = P2/T2,

The final temperature i.e the temperature at which the glass vessel can be shattered can be obtained as follow:

P1/T1 = P2/T2

0.850/300 = 2.45/T2

Cross multiply to express in linear form as shown below:

0.850 x T2 = 300 x 2.45

Divide both side by 0.850

T2 = (300 x 2.45) /0.850

T2 = 864.7K

Now let us convert 864.7K to celsius temperature. This is illustrated below:

°C = K - 273

°C = 864.7 - 273

°C = 591.7°C

Therefore, the temperature at which the glass vessel will shatter is 591.7°C

The temperature is 591.55 °C (or 864.7K)

Explanation:

Step 1: data given

Temperature = 27 °C = 300 K

The pressure = 0.850 atm

The vessel can withstand a pressure of 2.45 atm

Step 2: Guy-Lussac's law

Using Guy-Lussac's law (P1/T1) = (P2/T2) where temperature is measured in Kelvin (K = ºC +273), we can solve this problem.

P1/T1 = P2/T2

⇒with P1 = the initial pressure of the gas = 0.850 atm

⇒with T1 = the initial temperature = 300K

⇒with P2 = the max pressure the vessel ca nwithstand = 2.45 atm

⇒with T2 = the new temperature = TO BE DETERMINED

T2 = (P2*T1)/P1

T2 = (2.45 atm * 300K)/0.850 atm

T2 = 864.7 K = 591.55 °C

The temperature is 591.55 °C (or 864.7K)