The molar enthalpy of combustion of demand is -6.78KJ/mol.What mass of decane would have to be burned in order to raise the temperature of 500ml of water from 20 degrees Celsius to 55 degrees celsius. I tried using ndeltaH=mcdeltat. But it didn't work. Please help

To solve this problem, we need to use the equation:

q = mcΔT

Where:
q = heat absorbed or released by the system (in this case, the water)
m = mass of the water
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (Final temperature - Initial temperature)

First, we need to convert the given enthalpy of combustion from KJ/mol to J/mol. Since 1 KJ = 1000 J, the enthalpy becomes -6780 J/mol.

Next, we need to calculate the moles of decane required to produce this much energy. To do this, we can use the equation:

moles = energy / enthalpy

moles = -6780 J / -6.78 KJ/mol
= -6780 J / (-6.78 * 1000 J/mol)
≈ 1 mol

Since the molar mass of decane (C10H22) is 142.28 g/mol, the mass of decane required can be calculated by multiplying the moles by the molar mass:

mass = moles * molar mass
= 1 mol * 142.28 g/mol
= 142.28 g

Therefore, approximately 142.28 grams of decane would need to be burned to raise the temperature of 500 ml of water from 20 degrees Celsius to 55 degrees Celsius.

To solve this problem, we need to calculate the heat energy required to raise the temperature of water and then use the enthalpy of combustion of decane to find the mass of decane needed.

Let's break down the problem into steps:

Step 1: Calculate the heat energy required to raise the temperature of water.

The formula Q = m * c * ΔT is correct, where Q is the heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Given:
Mass of water (m) = 500 ml = 500 g (since 1 ml of water is approximately equal to 1 g)
Temperature change (ΔT) = 55°C - 20°C = 35°C
Specific heat capacity of water (c) = 4.18 J/g°C

Converting the temperature change to Kelvin:
ΔT = 35°C + 273.15 K = 308.15 K

Using the formula Q = m * c * ΔT, we can calculate the heat energy:
Q = 500 g * 4.18 J/g°C * 308.15 K

Step 2: Convert the heat energy to kilojoules (kJ).

1 J = 0.001 kJ
So, to convert Joules to kilojoules, divide by 1000.

Q(kJ) = (500 g * 4.18 J/g°C * 308.15 K) / 1000

Now, we have the heat energy in kilojoules.

Step 3: Use the enthalpy of combustion to find the mass of decane needed.

Given:
Molar enthalpy of combustion of decane = -6.78 kJ/mol

We can write the equation:
ΔH = Q / n

Where ΔH is the enthalpy change, Q is the heat energy, and n is the number of moles.

Rearranging the equation to solve for n:
n = Q / ΔH

Substituting the values:
n = Q(kJ) / (-6.78 kJ/mol)

Step 4: Calculate the mass of decane.

Since 1 mole of decane (C₁₀H₂₂) has a molar mass of 142.29 g/mol, we can calculate the mass of decane using the formula:
Mass = n × molar mass

Mass of decane = n × 142.29 g/mol

Substituting the value of n, we get:
Mass of decane = (Q(kJ) / -6.78 kJ/mol) × 142.29 g/mol

Solving this equation will give us the required mass of decane needed to raise the temperature of water.

Note: Please make sure to combine all the steps together and perform the calculations to get the final answer.