A sulfuric acid solution at 25 °C has a density of 1.27 g/mL. A

20.0-mL sample of this acid is measured out at 25 °C,
introduced into a 50-mL flask, and allowed to cool to 21 °C. The
mass of the flask plus solution is then measured at 21 °C. Use
the stated data, as necessary, to calculate the mass of the acid
sample.

density = mass x volume.

1.27 x 20.0 = ??
The remainder of the information is extraneous.

25.4

To calculate the mass of the acid sample, we need to know the mass of the flask plus the solution at 21 °C and the density of the sulfuric acid solution.

First, let's calculate the mass of the flask plus the solution at 21 °C. We have a 20.0-mL sample of acid, so the mass of this sample can be found by multiplying its volume by the density of the acid solution:

Mass of acid sample = Volume of acid sample × Density of acid solution

Since the density is given in grams per milliliter (g/mL), we can convert the volume to milliliters and then calculate the mass:

Volume of acid sample = 20.0 mL

Density of acid solution = 1.27 g/mL

Mass of acid sample = 20.0 mL × 1.27 g/mL

Next, we need to take into account the change in temperature. The mass of the flask plus the solution may change due to thermal expansion or contraction. However, we know that the density of a substance changes with temperature. Therefore, to accurately calculate the mass, we need to adjust for the change in density.

Let's say the mass we measured for the flask plus the solution at 21 °C is M grams. Since the density of the acid solution is given at 25 °C, we need to calculate the density of the acid solution at 21 °C. We can use the following formula to do that:

Density at 21 °C = Density at 25 °C × (1 + α × (T - T0))

Where α is the coefficient of thermal expansion and T0 is the reference temperature (25 °C in this case). The coefficient of thermal expansion for sulfuric acid is typically small, so we can approximate it as zero for simplicity.

Therefore, the formula becomes:

Density at 21 °C = Density at 25 °C

Since we are assuming no change in density with temperature, the mass of the acid sample will be the same as the mass of the flask plus the solution at 21 °C:

Mass of acid sample = M grams

So, to calculate the mass of the acid sample, you need to measure the mass of the flask plus the solution at 21 °C and assume that the density of the acid solution remains constant with temperature.