How long would it take for 1.50 moles of water at 100.0 to be converted completely into steam if heat were added at a constant rate of 19.0 j/s ?
If you look up the heat of vaporization per gram (Joul/g):
1. Change 1.5 moles of water to grams (multiply by 18.015 g/mol).
2. (grams)(joules/gram) ---> joules
3. joules / (joules/s) ---> seconds
If you look up the molar heat of vaporization of water (joules/mol):
1. (moles)(joules/mole) ---> joules
2. joules / (joules/s) ---> seconds
cannot get ans. please solve
To calculate the time it would take for 1.50 moles of water to be converted completely into steam, we need to use the equation:
q = mcΔT,
where:
q is the heat transferred,
m is the mass of the substance (water in this case),
c is the specific heat capacity of the substance (for water, it is 4.184 J/g°C),
and ΔT is the change in temperature.
First, we need to determine the heat required to convert the water into steam. The heat required for this phase change is known as the enthalpy of vaporization (ΔHvap), which for water is approximately 40.7 kJ/mol.
To convert ΔHvap from kJ/mol to J/molecule, we divide by Avogadro's number (6.022 x 10^23 molecules/mol). We get:
ΔHvap = (40.7 x 10^3 J/mol) / (6.022 x 10^23 molecules/mol)
Next, we need to calculate the total heat required to convert 1.50 moles of water into steam. This can be done by multiplying the number of moles (1.50) by the enthalpy of vaporization:
Total heat required = 1.50 moles x ΔHvap
Now that we have the total heat required, we can divide it by the heat added per second to find the time it will take:
Time = Total heat required / Heat added per second
Substituting the given values, we get:
Total heat required = (1.50 moles x ΔHvap) = (1.50 moles) x [(40.7 x 10^3 J/mol) / (6.022 x 10^23 molecules/mol)] = (1.50 moles) x (6.76 x 10^-20 J/molecule)
Time = (Total heat required) / (Heat added per second) = [(1.50 moles) x (6.76 x 10^-20 J/molecule)] / (19.0 J/s)
By evaluating this equation, you will find the time it will take for 1.50 moles of water to be converted completely into steam at a constant rate of 19.0 J/s.
To determine the time it would take for the given amount of water to be converted into steam, you need to calculate the amount of heat required and then divide it by the rate of heat addition.
First, let's determine the heat required to convert 1.50 moles of water into steam. To do this, we need to use the molar enthalpy of vaporization of water, which is the amount of energy required to convert one mole of liquid water into steam. The molar enthalpy of vaporization of water is 40.7 kJ/mol or 40,700 J/mol.
Since we have 1.50 moles of water, the total heat required is calculated as follows:
Heat = moles of water × molar enthalpy of vaporization
Heat = 1.50 mol × 40,700 J/mol
Next, we divide the total heat required by the rate of heat addition to find the time:
Time = Heat / Rate of heat addition
Time = (1.50 mol × 40,700 J/mol) / 19.0 J/s
Finally, we calculate the time:
Time = 64,050 J / 19.0 J/s
Therefore, it would take approximately 3,375 seconds (or 56.25 minutes) for 1.50 moles of water at 100.0°C to be completely converted into steam when heat is added at a constant rate of 19.0 J/s.