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kow [346]
3 years ago
6

If 75J of heat are applied to 8.4 L of a gas at 732 mmHg and 298K, what is the final temperature, in K, of the gas? Cp for an id

eal gas is 20.79 J/mol*K.
Chemistry
1 answer:
SVEN [57.7K]3 years ago
8 0

Answer:

309 K

Explanation:

Step 1: Convert the pressure to atm

We will use the conversion factor 1 atm = 760 mmHg.

732 mmHg × 1 atm/760 mmHg = 0.963 atm

Step 2: Calculate the moles (n) of the ideal gas

We will use the ideal gas equation.

P × V = n × R × T

n = P × V/R × T

n = 0.963 atm × 8.4 L/0.0821 atm.L/mol.K × 298 K

n = 0.33 mol

Step 3: Calculate the temperature change

We will use the following expression.

Q = n × Cp × ΔT

ΔT = Q/n × Cp

ΔT = 75 J/0.33 mol × 20.79 J/mol.K

ΔT = 11 K

Step 4: Calculate the final temperature

T = 298 K + 11 K = 309 K

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Answer: 0.245 moles of oxygen must be placed in the container to exert the given pressure at the given temperature. The Ideal Gas Law equation gives the relationship among the pressure, volume, temperature, and moles of gas.

Further Explanation:

The Ideal Gas Equation is:  

PV = nRT  

where:  

P - pressure (in atm)  

V - volume (in L)  

n - amount of gas (in moles)  

R - universal gas constant 0.08206 \frac{L-atm}{mol-K}  

T - temperature (in K)  

In the problem, we are given the values:  

P = 2.00 atm (3 significant figures)

V = 3.00 L  (3 significant figures)

n = ?

T = 25.0 degrees Celsius (3 significant figures)  

We need to convert the temperature to Kelvin before we can use the Ideal Gas Equation. The formula to convert from degree Celsius to Kelvin is:  

Temperature \ in \ Kelvin = Temperature\ in \ Celsius \ + \ 273.15  

Therefore, for this problem,  

Temperature\ in \ K = 25.0 +273.15\\Temperature\ in \ K = 298.15  

Solving for n using the Ideal Gas Equation:  

n \ = \frac{PV}{RT}\\n \ = \frac{(2.00 \ atm) \ (3.00 \ L)}{(0.08206 \ \frac{L-atm}{mol-K})( 298.15 \ K)}  \\n \ = 0.245 \ mol

The least number of significant figures is 3, therefore, the final answer must have only 3 significant figures.

Learn More  

1. Learn more about Boyle's Law brainly.com/question/1437490  

2. Learn more about Charles' Law brainly.com/question/1421697  

3. Learn more about Gay-Lussac's Law brainly.com/question/6534668

Keywords: Ideal Gas Law, Volume, Pressure

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