Question

A two-liter soft drink bottle can withstand apressure of

Answer 1

Explanation:

According to the ideal gas equation, PV = nRT.

where,     P = pressure,        V = volume

               n = no. of moles,      R = gas constant

               T = temperature

Also, density is equal to mass divided by volume. And, no. of moles equals mass divided by molar mass.

Therefore, then formula for ideal gas could also be as follows.

                 P = $\frac{mass}{volume \times molar mass} \times RT$

or,             P = $\frac{density}{\text{molar mass}} \times RT$

Since, density is given as 0.789 g/ml which is also equal to 789 g/L (as 1000 mL = 1 L). Hence, putting the given values into the above formula as follows.

               P = $\frac{density}{\text{molar mass}} \times RT$

                  = $\frac{789 g/l}{46.06 g/mol} \times 0.0821 L atm/mol K \times 373 K$

                  = 525 atm

As two-liter soft drink bottle can withstand a pressure of  5 atm and the value of calculated pressure is 525 atm which is much greater than 5 atm.

Therefore, the soft drink bottle will  obviously explode.