Question

the partial pressure of oxygen in the atmosphere is 159. torr. calculate the partial pressure in mmhg and atm. round each of your answers to 3 significant digits.

Explanation:

Step1: Convert torr to mmHg

We know that 1 torr = 1 mmHg. So, the partial pressure in mmHg is the same as in torr.
$159. \text{ torr} = 159. \text{ mmHg}$ (rounded to 3 significant digits, it remains 159 mmHg as the original value has 3 significant digits? Wait, 159. has three significant digits? Wait, 159. torr: the decimal after 9 indicates that 1,5,9 are significant, so three significant digits. So 159 torr is 159 mmHg.

Step2: Convert torr to atm

We know that 1 atm = 760 torr. So, to convert torr to atm, we use the formula: $\text{Pressure (atm)} = \frac{\text{Pressure (torr)}}{760}$
So, $\text{Pressure (atm)} = \frac{159.}{760}$
Calculate that: $159 \div 760 \approx 0.20921...$
Round to 3 significant digits: 0.209 atm (wait, 0.209? Wait, 159 has three significant digits, so the result should have three. Let's calculate 159/760:

159 ÷ 760: 760 × 0.2 = 152, 159 - 152 = 7, so 0.2 + 7/760 ≈ 0.2 + 0.00921 = 0.20921, which rounds to 0.209 atm (three significant digits: 2,0,9? Wait, 0.209: the first non-zero digit is 2, then 0, then 9. So three significant digits.

Wait, but let's check the calculation again. 159 divided by 760:

159 ÷ 760 = 0.209210526...

Rounded to three significant digits: look at the fourth digit, which is 2, so we don't round up the third. So 0.209 atm.

Wait, but maybe I made a mistake. Let's recalculate:

159 ÷ 760:

760 × 0.2 = 152

159 - 152 = 7

7/760 = 0.0092105

So total is 0.2 + 0.0092105 = 0.2092105, which is 0.209 when rounded to three significant digits (since the fourth digit is 2, less than 5, so we keep the third digit as 9).

Answer:

mmHg: 159 mmHg
atm: 0.209 atm