You have a 46.0 G sample of H20 at a temperature of -58.0*C. How many joules of energy are needed to heat the ice to 95.3*C?

To calculate the amount of energy needed to heat the ice to a higher temperature, we can use the equation:

Q = mcΔT

Where:
Q represents the amount of energy needed (in joules),
m represents the mass of the substance (in grams),
c represents the specific heat capacity of the substance (in joules per gram per degree Celsius), and
ΔT represents the change in temperature (in degrees Celsius).

In this case, we have a 46.0 g sample of H2O (water) at a temperature of -58.0°C, and we want to heat it to 95.3°C.

First, we need to calculate the energy required to heat the ice from -58.0°C to the freezing point of water, which is 0.0°C. Since water is in the solid state (ice) during this temperature range, we need to use the specific heat capacity of ice, which is approximately 2.09 J/g°C.

ΔT1 = (0.0°C - (-58.0°C)) = 58.0°C

Q1 = m * c1 * ΔT1
Q1 = 46.0 g * 2.09 J/g°C * 58.0°C

Next, we need to calculate the energy required to melt the ice. To transition from ice to water, we need to consider the heat of fusion, which is the amount of energy required to change a substance from a solid to a liquid. For water, the heat of fusion is 334 J/g.

Q2 = m * heat of fusion
Q2 = 46.0 g * 334 J/g

Finally, we need to calculate the energy required to heat the water from 0.0°C to 95.3°C. Once the ice is completely melted, we can use the specific heat capacity of liquid water, which is approximately 4.18 J/g°C.

ΔT3 = (95.3°C - 0.0°C) = 95.3°C

Q3 = m * c3 * ΔT3
Q3 = 46.0 g * 4.18 J/g°C * 95.3°C

To find the total amount of energy required, we sum up Q1, Q2, and Q3:

Total energy = Q1 + Q2 + Q3

Calculate each of these values using the given formulas and then sum them to find the total energy required in joules.

q1 = mass ice x specific heat ice x (Tfinal-Tinitial)

q2 = mass ice x heat fusion

q3 = mass water x specific heat water x (Tfinal-Tinitial)
Total Q = q1 + q2 + q3