In an attempt to determine an accurate value of the gas constant, R, a student heated a container of volume 20.000dm³ filled with 0.251 32g of helium gas to 500°C and measured the pressure as 206.402 cm of water in a manometer at 25°C. Calculate the value of R from these data. (The density of water at 25°C is 0.997 07 g cm⁻³; the construction of a manometer is described in Exercise 1.6(a).)

Data in  Exercise 1.6(a)

A manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid. Suppose the liquid is water, the external pressure is 770 Torr, and the open side is 10.0 cm lower than the side connected to the apparatus. What is the pressure in the apparatus? (The density of water at 25°C is 0.997 07 g cm⁻³.)