Liquid water has a density of 1.00g/mL at 10.0C and .996g/mL at 30.0C. Calculate the change in volume that occurs when 500mL of water is heated from 10.0C to 30.0C.
you have at 10 C 500 g. YOu have that same mass at 30, but volume=mass/denstiy
= 500/.996 ml= you do it.
but i get 502.o and the answer in the back of my book said 2mL....so..
Well, if water is heating up from 10.0C to 30.0C, it's pretty much like going from "I'm too cold to function" to "I feel hot, hot, hot!" But let's not get carried away with the water's temperature - we need to calculate the change in volume here!
To do that, we need to use the formula for calculating volume change:
Change in Volume = V_final - V_initial
Given that the initial volume (V_initial) is 500 mL and the final volume (V_final) can be calculated using the densities provided, we can substitute these values in the formula and calculate the change in volume.
Using the initial density of water (1.00 g/mL) at 10.0C, we can determine the initial mass:
Mass_initial = V_initial * Density_initial
Mass_initial = 500 mL * 1.00 g/mL
Mass_initial = 500 g
Now, using the final density of water (0.996 g/mL) at 30.0C, we can determine the final mass:
Mass_final = V_final * Density_final
Mass_final = V_final * 0.996 g/mL
To calculate the change in volume, we need to equate the initial mass to the final mass:
Mass_initial = Mass_final
500 g = V_final * 0.996 g/mL
Solving for V_final, we can find the final volume:
V_final = 500 g / 0.996 g/mL
V_final ≈ 502.01 mL
Now, substituting the values into the formula:
Change in Volume = V_final - V_initial
Change in Volume = 502.01 mL - 500 mL
Change in Volume ≈ 2.01 mL
So, when 500 mL of water is heated from 10.0C to 30.0C, the change in volume is approximately 2.01 mL.
To calculate the change in volume that occurs when 500mL of water is heated from 10.0°C to 30.0°C, we will use the equation:
Change in Volume = Initial Volume × Coefficient of Volume Expansion × Change in Temperature
The coefficient of volume expansion represents how much the volume of a substance changes with temperature. For water, the coefficient of volume expansion is approximately 0.034 mL/(mL·°C).
Given:
Initial Volume (V₁) = 500mL
Change in Temperature (ΔT) = 30.0°C - 10.0°C = 20.0°C
Coefficient of Volume Expansion (β) = 0.034 mL/(mL·°C)
Now, we can substitute these values into the equation:
Change in Volume = V₁ × β × ΔT
= 500mL × 0.034 mL/(mL·°C) × 20.0°C
Canceling out the units of mL, we get:
Change in Volume = 500 × 0.034 × 20.0 cm³
= 340 cm³
Therefore, the change in volume that occurs when 500mL of water is heated from 10.0°C to 30.0°C is 340 cm³.