Hydrogen gives off 120. J/g of energy when burned in oxgyen, and methane gives off 50. J/g under the same circumstances. If the mixture of 5.0 g of hydrogen and 10. g of methane is burned, and the heat released is transferred to 50.0 g of water at 25.0 degress Celsius, what final temperature will be reached by the water?
120 J/g x 5.0 g hydrogen = ?? J.
50 J/g x 10.0 g methane = ?? J.
total = ?? J = q
mass water x specific heat water x (Tfinal-Tinitial) = q
Solve for Tfinal.
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30.26 degrees celsius
30.3 degrees celsius
Well, it seems like we have a fiery situation on our hands! Let's do some math and heat up the fun.
First, let's calculate the energy released from burning 5.0 g of hydrogen. Multiplying the mass by the energy released per gram, we get: 5.0 g hydrogen * 120 J/g = 600 J of energy released.
Next, let's calculate the energy released from burning 10.0 g of methane: 10.0 g methane * 50 J/g = 500 J of energy released.
Now, let's add up the total energy released from both hydrogen and methane: 600 J + 500 J = 1100 J.
To find the final temperature reached by the water, we'll use the heat capacity formula Q = mcΔT, where Q is the heat (in Joules), m is the mass (in grams), c is the specific heat capacity (in J/g°C), and ΔT is the change in temperature (in Celsius).
Since we know the heat energy released (1100 J), the mass of water (50.0 g), and the starting temperature (25.0°C), we can rearrange the formula as ΔT = Q / (mc).
ΔT = 1100 J / (50.0 g water * c water)
Now, we need to find the specific heat capacity of water. If only we had a joke to lighten the mood while we look it up...
Why did the scarecrow become a successful comedian? Because he was outstanding in his field!
Ahem, sorry about that. Back to the calculations!
The specific heat capacity of water is approximately 4.184 J/g°C. Plugging in the values, we get:
ΔT = 1100 J / (50.0 g * 4.184 J/g°C)
Calculating this out, we find:
ΔT ≈ 5.26°C
Finally, to find the final temperature, we add the change in temperature to the initial temperature:
Final temperature = 25.0°C + 5.26°C ≈ 30.26°C
So, the water will reach a final temperature of approximately 30.26 degrees Celsius. Just don't forget to bring the marshmallows for this hot water party!
To find the final temperature reached by the water, we need to calculate the amount of heat released by burning the mixture of hydrogen and methane, and then use that heat to determine the temperature increase of the water.
First, let's calculate the heat released by burning the mixture of hydrogen and methane.
1. Calculate the heat released by 5.0 g of hydrogen:
Heat released by hydrogen = mass of hydrogen * heat of combustion of hydrogen
Heat released by hydrogen = 5.0 g * 120 J/g
Heat released by hydrogen = 600 J
2. Calculate the heat released by 10.0 g of methane:
Heat released by methane = mass of methane * heat of combustion of methane
Heat released by methane = 10.0 g * 50 J/g
Heat released by methane = 500 J
3. Calculate the total heat released by the mixture:
Total heat released = heat released by hydrogen + heat released by methane
Total heat released = 600 J + 500 J
Total heat released = 1100 J
Now that we have the total heat released, we can use it to determine the temperature increase of the water.
4. Calculate the heat capacity of water:
Heat capacity of water = mass of water * specific heat capacity of water
Heat capacity of water = 50.0 g * 4.184 J/g°C
Heat capacity of water = 209.2 J/°C
5. Calculate the temperature increase of the water:
Temperature increase = Total heat released / Heat capacity of water
Temperature increase = 1100 J / 209.2 J/°C
Temperature increase ≈ 5.26°C
6. Finally, calculate the final temperature reached by the water:
Final temperature = Initial temperature + Temperature increase
Final temperature = 25.0°C + 5.26°C
Final temperature ≈ 30.26°C
Therefore, the final temperature reached by the water will be approximately 30.26°C.