Question

density
which has the greater mass, air or lead? most would answer lead, but this question actually does not have an answer. to compare these two things, you need to know how much of each you have. a large amount of air could have a greater mass than a small amount of lead. to compare different things, we have to compare the masses of each that occupy the same space, or volume. this is called density. it is measured in units of g/ml or g/cm³.
density = mass/volume or d = m/v
solve each problem.
what is the density of carbon dioxide gas if 0.196 g occupies a volume of 100 ml? the density formula is d = m/v
a block of wood that measures 3.0 cm on each side has a mass of 27 g. what is the density of the block?

Explanation:

Step1: Identify the density formula

The formula for density is $D=\frac{M}{V}$, where $D$ is density, $M$ is mass and $V$ is volume.

Step2: Solve for the density of carbon - dioxide

Given $M = 0.196\ g$ and $V=100\ mL$. Substitute into the formula: $D=\frac{0.196\ g}{100\ mL}=0.00196\ g/mL$.

Step3: Calculate the volume of the wooden block

The wooden block is a cube with side length $s = 3.0\ cm$. The volume of a cube $V=s^3=(3.0\ cm)^3 = 27\ cm^3$. Given $M = 27\ g$. Using the density formula $D=\frac{M}{V}=\frac{27\ g}{27\ cm^3}=1\ g/cm^3$.

Step4: Determine the volume of the irregular - shaped stone

The volume of the stone is equal to the volume of water displaced. The initial volume of water is not given completely, but if the water level rose from an initial volume (say $V_1$) to $V_2 = 7.0\ mL$ and the volume of water added is $2.0\ mL$, then the volume of the stone $V = 7.0\ mL- (7.0\ mL - 2.0\ mL)=2.0\ mL$. Assume the mass of the stone is $m$ (not given in the problem - if we had the mass, we could calculate density as $D=\frac{m}{V}$).

Answer:

The density of carbon - dioxide gas is $0.00196\ g/mL$. The density of the wooden block is $1\ g/cm^3$. For the irregular - shaped stone, we need the mass to calculate density completely, but its volume is $2.0\ mL$.