Density Calculation | MCQs

Explanation

The formula for calculating the density of an ideal gas is d = PM/RT, where: 

• d: is the density of the gas
• P: is the pressure of the gas
• M: is the molar mass of the gas
• R: is the ideal gas constant
• T: is the temperature of the gas in Kelvin

The ideal gas law is expressed as PV = nRT, where 'n' is the number of moles.

Density (d) is mass (m) divided by volume (V), so d = m/V.

We can relate the number of moles (n) to mass (m) and molar mass (M) using n = m/M.

Substituting this into the ideal gas law, we get PV = (m/M)RT.

Rearranging the equation to solve for density (d = m/V), we get d = PM/RT. 

Explanation

To find the density of the steel balls, we need to use the formula for density:

Density = Mass/Volume

1. Calculate the total mass of the steel balls:

Each ball has a mass of 27 g, and there are 10 balls.

Total mass = 10 x 27 = 270 g

2. Calculate the volume displaced by the steel balls:

The initial volume of water is 20 cm^3

The final volume of water is 50 cm^3

The volume displaced by the steel balls is:

Volume displaced = 50 cm^3 - 20 cm^3 = 30 cm^3

3. Calculate the density of the steel:

Using the total mass and the volume displaced:

Density = 270 g / 30cm,^3 = 9.0 g/cm^3

Therefore, the density of the steel is 9.0 g/cm^3.