A 10.0 cm long cylindrical glass tube, sealed at one end, is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 11.82 g . The density of ethanol is 0.789 g/mL. Calculate the inner diameter of the tube in centimeters.
What's the volume of the ethanol?
mass = volume in mL x density in g/mL
11.82 g = volume in mL x 0.789 g/mL
volume = 11.82/0.789 = about 15 but you need to redo all of these calculations.
Since the ethanol filled the container that is the volume of the container.
Vcontainer = pi*r^2*h.
You know volume, you know pi, you know h, substitute and solve for r. Then diameter is 2*radius.
Post your work if you get stuck.
To calculate the inner diameter of the tube, we need to use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height of the cylinder.
First, let's convert the length of the cylinder to meters, as it is given in centimeters:
Length (h) = 10.0 cm = 0.1 m
Next, we can calculate the volume of the cylinder using the given mass and density of ethanol:
Density = mass / volume
Therefore, the volume of ethanol in the cylinder (V) can be found using the equation:
Volume = mass / density = 11.82 g / 0.789 g/mL
Let's convert the density to g/cm³ to match the units of mass:
Density = 0.789 g/mL = 0.789 g/cm³
So, the volume of ethanol in the cylinder is:
Volume = 11.82 g / 0.789 g/cm³ = 14.98 cm³
Now, we can substitute the values of volume and height into the volume formula to solve for the radius:
14.98 cm³ = πr^2 * 0.1 m
We convert the volume to m³ to match the unit of height:
14.98 cm³ = 0.01498 m³
Rearranging the formula, we get:
r^2 = (0.01498 m²) / (π * 0.1 m)
Simplifying the equation:
r^2 = 0.150653
Taking the square root of both sides:
r ≈ 0.3877 m
Finally, we can convert the radius to centimeters:
Radius (r) ≈ 0.3877 m * 100 cm/m ≈ 38.77 cm
The inner diameter of the tube is double the radius, so:
Inner Diameter ≈ 38.77 cm * 2 ≈ 77.54 cm
Therefore, the inner diameter of the glass tube is approximately 77.54 cm.