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What is the pressure of 4 moles of helium in a 50 L tank at 308 K?
Use PV = nRT.
A. 24.64 atm
B. 0.13 atm
O C. 0.51 atm
D. 2.02 atm

Sagot :

Polyblock

Answer:

D

Explanation:

P = Pressure

V = Volume

n = Moles

R = .08206 (because we're using liters)

T = Temperature (as K)

P(50) = (4)(.08206)(308)

P(50) = 101.09792

Divide both sides by 50

P(50)/50 = 101.09792/50

P = 2.0219584

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf D. \ 2.02 \ atm}}[/tex]

Explanation:

We are asked to find the pressure of helium gas using the ideal gas law.

[tex]PV= nRT[/tex]

In this formula P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature.

The pressure is unknown and we are solving for it. The volume is 50 liters, there are 4 moles of helium gas, the universal gas constant is 0.08206 L *atm/ mol * K, and the temperature is 308 Kelvin.

[tex]\bullet \ V= 50 \ L \\\bullet \ n= 4 \ mol \\\bullet \ R = \frac {0.08206 \ L * atm}{mol *K}\\\bullet \ T= 308 \ K[/tex]

Substitute these values into the formula.

[tex]P * 50 \ L= 4 \ mol * \frac {0.08206 \ L * atm}{mol *K} * 308 \ K[/tex]

Multiply on the right side. The units of moles (mol)  and Kelvin (K) cancel each other out.

[tex]P* 50 \ L = 4 * 0.08206 \ L *atm * 308[/tex]

[tex]P*50 \ L =0.32824 \ L * atm *308[/tex]

[tex]P* 50 \ L = 101.09792 \ L * atm[/tex]

We are solving for the pressure, so we must isolate the variable P. It is being multiplied by 50 liters. The inverse operation of multiplication is division, so divide both sides by 50 L.

[tex]\frac {P* 50 \ L}{50 \ L} = \frac {101.09792 \ L * atm}{50 \ L}[/tex]

[tex]P= \frac {101.09792 \ L * atm}{50 \ L}[/tex]

The units of liters (L) cancel.

[tex]P= \frac{101.09792}{50 } \ atm[/tex]

[tex]P= 2.0219584 \ atm[/tex]

If we round to the nearest hundredth place the 1 in the thousandth place tells us to leave the 2 in the hundredth place.

[tex]P \approx 2.02 \ atm[/tex]

The pressure is approximately 2.02 atmospheres and choice D is correct.

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