Question

The pressure of a gas sample was measured to be 654 mmhg. What is the pressure in kpa? (1 atm = 1. 01325 × 10 5 pa)

Answer 1

Taking into account the change of units, the pressure of the gas sample is 87.19 kPa.

What is rule of three

In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: $c=\frac{cxb}{a}$

Pressure

The direct rule of three is the rule applied in this case where there is a change of units.

To perform in this case the conversion of units, you must first know that:

• 1 atm= 760 mmHg
• 1 atm = 1. 01325×10⁵ Pa= 101325 Pa
• 1 kPa= 1000 Pa

So, if 1 atm is 760 mmHg, how many atm equals 654 mmHg?

760 mmHg ⇒ 1 atm

654 mmHg ⇒ x

So: $x=\frac{654 mmHgx1 atm}{760 mmHg}$

Solving:

x=0.86 atm

Now, if 101325 Pa are 1 atm, how many Pa equals 0.86 atm?

1 atm ⇒ 101325 Pa

0.86 atm ⇒ x

So: $x=\frac{0.86 atmx101325 Pa}{1 atm}$

Solving:

x= 87,192.83 Pa

Finally, if 1 kPa is 1000 Pa, how many kPa equals 87,192.83 Pa?

1000 Pa ⇒ 1 kPa

87,192.83 Pa ⇒ x

So: $x=\frac{87,192.83 Pax1 kPa}{1000 Pa}$

Solving:

x=87.19283 kPa≅ 87.19 kPa

In summary, the pressure of the gas sample is 87.19 kPa.

Learn more with this example:

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