a 0.0500 mol sample of a nutrient substance is burned in a bomb calorimeter containing 2.00 x 10^2g H2O. If the formula weight of this nutrient substance is 114g/mol, what is the fuel value (in nutrient Cal) if the temperature of the water increased 5.70C
To calculate the fuel value in nutrient calories, we can use the following formula:
Fuel Value (in nutrient Cal) = (Heat transferred to water) / (Amount of substance burned)
First, let's calculate the heat transferred to the water.
1. Determine the specific heat capacity of water. The specific heat capacity of water is 4.18 J/g°C.
2. Convert the mass of water from grams to kilograms:
Mass of water = 2.00 x 10^2 g = 2.00 x 10^(-1) kg
3. Calculate the heat transferred to the water:
Heat transferred to water = (Mass of water) x (Specific heat capacity of water) x (Change in temperature)
= (2.00 x 10^(-1) kg) x (4.18 J/g°C) x (5.70°C)
= (2.00 x 10^(-1) kg) x (4.18 J/g°C) x (5.70°C)
= 4.7536 Joules
Next, let's calculate the amount of substance burned.
1. Convert the molar amount of the nutrient substance from moles to grams:
Mass of nutrient substance = 0.0500 mol x (114 g/mol)
= 5.70 g
2. Calculate the amount of substance burned:
Amount of substance burned = 5.70 g
Now we can calculate the fuel value:
Fuel Value (in nutrient Cal) = (Heat transferred to water) / (Amount of substance burned)
= 4.7536 Joules / 5.70 g
= 4.7536 J/g
Therefore, the fuel value (in nutrient Cal) is approximately 4.7536.
To find the fuel value, we need to calculate the heat released from burning the nutrient substance, which can be determined using the heat capacity of water and the temperature increase.
The heat released (q) can be calculated using the equation:
q = m * c * ΔT
where:
q is the heat released (in Joules or calories)
m is the mass of water (in grams)
c is the specific heat capacity of water (1 cal/g·°C or 4.184 J/g·°C)
ΔT is the temperature increase (in °C)
First, let's convert the 0.0500 mol sample into grams using the formula weight of the nutrient substance (114 g/mol):
Mass of nutrient substance = number of moles * formula weight
Mass of nutrient substance = 0.0500 mol * 114 g/mol
Next, let's calculate the heat released (q):
q = m * c * ΔT
In this case, the mass of water (m) is given as 2.00 x 10^2g, and the temperature increase (ΔT) is given as 5.70°C.
Substituting the values into the equation:
q = 2.00 x 10^2g * 1 cal/g·°C * 5.70°C
Calculating this, we get:
q = 1140 cal
Therefore, the fuel value is 1140 nutrient calories.
mols sample = 0.05/114 = approx (but you do it for the real number) = 0.00044
q = mass H2O x specific heat H2O x delta T.
q = 200g x 1 cal/g*C x 5.7
q = approx 1100 calories for 0.05g or
1100/0.05 = approx 23000 calories
23,000 calories x (1 kcal/1000 cal) = 23 kcal = 23 nutrient calories.