Question

convert the following pressures to the desired unit. show your work. use a calcul. 1 atm = 760 mmhg = 760 torr = 101.3 kpa = 14.7 psi

1. convert 3.2 atm to mmhg.
2. convert 800 mmhg to atm.
3. convert 1500 torr to kpa.
4. convert 25 kpa to psi.
5. convert 5.0 atm to torr.
6. convert 1500 psi to atm.
7. convert 760 mmhg to kpa.
8. convert 1.2 atm to psi.
9. convert 830 torr to atm.
10. convert 100 kpa to mmhg.

Explanation:

Step1: Recall conversion factor

Given $1\ atm = 760\ mmHg$. To convert $3.2\ atm$ to $mmHg$, multiply by the conversion - factor.
$3.2\ atm\times760\frac{mmHg}{atm}=2432\ mmHg$

Step2: Recall conversion factor for second problem

Given $1\ atm = 760\ mmHg$. To convert $800\ mmHg$ to $atm$, divide by the conversion - factor.
$800\ mmHg\times\frac{1\ atm}{760\ mmHg}\approx1.053\ atm$

Step3: Recall conversion factor for third problem

Given $1\ atm = 760\ Torr=101.3\ kPa$. First, find the relationship between Torr and kPa: $1\ Torr=\frac{101.3}{760}\ kPa$. To convert $1800\ Torr$ to $kPa$, multiply by the conversion - factor.
$1800\ Torr\times\frac{101.3}{760}\ kPa\approx240.4\ kPa$

Step4: Recall conversion factor for fourth problem

Given $1\ atm = 101.3\ kPa = 14.7\ psi$. First, find the relationship between kPa and psi: $1\ kPa=\frac{14.7}{101.3}\ psi$. To convert $25\ kPa$ to $psi$, multiply by the conversion - factor.
$25\ kPa\times\frac{14.7}{101.3}\ psi\approx3.63\ psi$

Step5: Recall conversion factor for fifth problem

Given $1\ atm = 760\ Torr$. To convert $5.0\ atm$ to Torr, multiply by the conversion - factor.
$5.0\ atm\times760\frac{Torr}{atm}=3800\ Torr$

Step6: Recall conversion factor for sixth problem

Given $1\ atm = 14.7\ psi$. To convert $1500\ psi$ to $atm$, divide by the conversion - factor.
$1500\ psi\times\frac{1\ atm}{14.7\ psi}\approx102.04\ atm$

Step7: Recall conversion factor for seventh problem

Given $1\ atm = 760\ mmHg = 101.3\ kPa$. First, find the relationship between mmHg and kPa: $1\ mmHg=\frac{101.3}{760}\ kPa$. To convert $700\ mmHg$ to $kPa$, multiply by the conversion - factor.
$700\ mmHg\times\frac{101.3}{760}\ kPa\approx93.6\ kPa$

Step8: Recall conversion factor for eighth problem

Given $1\ atm = 14.7\ psi$. To convert $1.2\ atm$ to $psi$, multiply by the conversion - factor.
$1.2\ atm\times14.7\frac{psi}{atm}=17.64\ psi$

Step9: Recall conversion factor for ninth problem

Given $1\ atm = 760\ Torr$. To convert $830\ Torr$ to $atm$, divide by the conversion - factor.
$830\ Torr\times\frac{1\ atm}{760\ Torr}\approx1.092\ atm$

Step10: Recall conversion factor for tenth problem

Given $1\ atm = 760\ mmHg = 101.3\ kPa$. First, find the relationship between kPa and mmHg: $1\ kPa=\frac{760}{101.3}\ mmHg$. To convert $100\ kPa$ to $mmHg$, multiply by the conversion - factor.
$100\ kPa\times\frac{760}{101.3}\ mmHg\approx750.2\ mmHg$

Answer:

1. $2432\ mmHg$
2. $\approx1.053\ atm$
3. $\approx240.4\ kPa$
4. $\approx3.63\ psi$
5. $3800\ Torr$
6. $\approx102.04\ atm$
7. $\approx93.6\ kPa$
8. $17.64\ psi$
9. $\approx1.092\ atm$
10. $\approx750.2\ mmHg$