a sample of H2O with a mass of 46.0 grams has a temperature of -58.0 degress celcius. how many joules of energy are necessary to melt 46.0 grams of ice?

Note the correct spelling of celsius.

q to move temperature of ice from -58 to zero.
q = mass ice x specific heat ice x [Tfinal-Tinitial].
Tfinal is zero and Tinitial is -58.

q to melt the ice.
q = mass ice x heat fusion.

total Q = q1 + q2.

To calculate the amount of energy required to melt a given mass of ice, you can use the equation:

Q = m × ΔHf,

where Q is the energy in Joules, m is the mass of the ice in grams, and ΔHf is the heat of fusion, which is the amount of energy required to change the state of a substance from solid to liquid at a specific temperature.

For water, the heat of fusion (ΔHf) is 334 J/g.

In this case, the mass of the ice is given as 46.0 grams. So, we can substitute these values into the equation:

Q = 46.0 g × 334 J/g.

Now we can solve the equation to find the energy required:

Q = 46.0 g × 334 J/g = 15,364 J.

Therefore, it takes approximately 15,364 Joules of energy to melt 46.0 grams of ice.